Any Unique pokeballs?

Quite a number of them. There are a variety of standard-issue balls, as well as custom and unique ones used by different factions and groups.

A note on Poké Ball function: Poké Balls are not normally broken or wasted after a single use; if they fail, then they can be retrieved, and as long as their charge hasn't been expended entirely or the hinge hasn't broken, they can be reused. If they are drained, they can be recharged at a Pokémon Center or hotel.

A note on Water-type Pokémon and how they function: A common problem with perception of how Poké Balls work is the idea that Water-type, swimming Pokémon wouldn't be able to function normally on land. In my setting, alongside the capture, teleportation and containment fields the Poké Ball can also produce a support field. This allows the ball to draw a portion of necessary environmental conditions through to support the Pokémon that has been brought into battle. This would be a sphere of water large enough for the given Pokémon to survive, an area of superheated air for some Fire-types, so on and so forth. The ball itself supports the field, running on special internal reactant that can be recharged when the ball is recharged. Thusly, land-combat with Water-types is feasible, I.E. a Seaking can be summoned in a sphere of water that moves with the Pokémon so it can fight effectively.

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Common Ball Variants found in the Ōshū region:

1: Melody Ball.
Coloration: Teal cap with bronze musical around the rim; white bottom, as well as standard white trigger button.
Usage: Melody Balls play soothing music when a Pokémon is captured, helping to calm more temperamental and rowdy Pokémon to ease capture. Commonly used by trainers in the Collines Verdes region, they're also used as an aesthetic choice by "Beauty Trainers", looking to have an attractive Poké ball for display purposes when they enter contests. The Collines Verdes region is the center of Ōshū "Poké-Fashion" and competitions for beauty and Pokémon talent, after all.
Cost: 350 Poké dollars, somewhat more than common Poké balls.

2: Wide Ball
Coloration: Bright yellow cap and black underside; bright blue "fan" pattern radiation from the white trigger button up over the cap, all the way to the rear hinge. Nearly twice the size of a normal ball, they're intended to be tossed like one might throw a dodge ball.
Usage: Wide Balls are unique in that they're one of, if not the only, commonly available wide-dispersion Poké balls on the market. They aren't normally used in standard combat, but rather used as a means of capturing and cataloging large numbers of low-level Pokémon in a single toss. They're commonly used in Ulimaroa and Grabenfeld, both locations where large groups of small, fast-moving Pokémon can cause trouble for Trainers and civilians alike.
Cost: 700 Poké dollars; also have to be bought through specialty retailers.

3: Thunder Ball
Coloration: Electric yellow with gold lightning streaks emblazoned across the entire surface; glowing trigger button.
Usage: Thunder Balls are special "enhanced" balls, a common form of Poké balls found in the region. They have the special trait of carrying a small electrical charge generator alongside their normal core components which causes a stunning effect when the ball contacts a weakened Pokémon. Though some types are obviously immune, this does make catching Electric-weak Pokémon easier, particularly in the case of Water-types.
Cost: 500 Poké dollars each.

4: Blast Ball
Coloration: Magma red and orange with an underside the color of coal. Glowing orange trigger button.
Usage: Blast Balls are another "enhanced" ball, this time featuring a thermal generator that will hit a weakened Pokémon with a low-powered burst of heat. Again, this is useless against typings that are resistant to Fire-type damage, but helps to daze, disorient and further weaken those weak to the given element, especially Grass-types.
Cost: 500 Poké dollars each.

5: Solar Ball
Coloration: Sky blue with a sunburst pattern in metallic gold on top; warm yellow glow to the trigger button and earthy green underside.
Usage: Solar Balls are a unique evolution of the previous Dusk Ball. Originally developed by Silph Co. to fill a niche opposite the Dusk Ball, the Solar Ball is actually a solar powered device that, if used after charging in sunlight, is much more effective than a regular ball, though less so than a Great Ball. The Solar Ball also maintains a charge in dark environments, though is only as good as a regular ball in those circumstances. The main benefit of using them in the dark is that they create a warm, comforting glow when held or thrown, acting as a viable light source in caves and dark interiors.
Cost: 275 Poké dollars each; not too much more expensive than normal balls.

6: Pierce Ball
Coloration: Black top cap and bottom as well, with red trim along the seam and a very brightly glowing red trigger button. Makes a distinctive high-pitched whistle when thrown.
Usage: Pierce Balls are made to penetrate psychic shields and physical barriers thrown up by Pokémon, generating a unique energy field that interacts with both energy and inorganic materials. If a Rock-Type throws up a slab of stone, or a Psychic-type tries to deflect a ball with a wave of power, the Pierce Ball will rifle straight through the obstruction and hit the mark. The one downside is the power expenditure means that it will burn out after a single use, and cannot be retrieved if it fails.
Cost: 400 Poké dollars each.

7: Cold Snap Ball
Coloration: Solid white cap and bottom with a blue snowflake over-pattern on the cap. Glowing blue trigger button.
Usage: The Cold Snap Ball was developed as a specialty device for Opoc Trainers. These balls are made to perform significantly better against Ice-type Pokémon and in cold weather, with even colder temperatures charging the ball further. The end result is a powerful ball for capturing Pokémon native to the mountainous wilderness of Northern Opoc, and even against other typings it proves to be very effective. They are, however, exorbitantly expensive, and become LESS effective in hot weather.
Cost: 925 Poké dollars each; must be purchased in Opoc region or ordered specially through one of the major digital purchase platforms (Sukaitawā Technical Corp's Crystalink shopping system, Silph Co.'s Silph-Shop Pokédex App, and The Triple P Digi-store, all available in standard Pokédexes, Triple P-made Trainer Bands, and Sukaitawā Technical Corp's new Crystalis Array System.)

8: Military Issue Ball:
Coloration: Camo-colored, in a variety of environmental formats. Common colors include blue-white-grey "Ocean Camo" in Grabenfeld, tan-red-yellow "Desert Camo", and green-grey-brown "Alpine" colors. No trigger light.
Usage: Military Issue Balls are produced and distributed as standard issue gear for government funded and supported trainers, particularly in the International Police Force. These balls are lighter than standard, usually with textured caps to make usage with gloves easier. They are also significantly more durable, and have larger battery reserves. They are somewhat stronger than normal balls, with a more steady and stable capture field.
Cost: Mass-produced, available in military regions through proper sources as a reward, and surplus stores throughout other countries at roughly 300 per ball.

9: Lust Ball
Coloration: Metallic black and grey, bright purple trigger button. Usually inlaid with designs either of Team Concupi, or of a heart set into the cap in metallic purple. Releases a cloud of purple smoke when triggered.
Usage: Lust Balls are dubious creations made by Team Concupi researchers to further their Poképhiliac agenda. The balls are actually stolen and heavily repurposed technology, a combination of components Friend Balls, Love Balls and Luxury Balls that impress a deep, abiding affection for the owner of the Pokémon...To the point of nearly brainwashed lust. The balls are very powerful, and the influence of them is difficult to break. They release a powerful aphrodisiac gas made up of Pokémon pheromones, human pheromones and several illicit chemicals that can have long-term personality warping impact on any Pokémon captured via the Lust Ball.
Cost: Black-market only, 700 Poké dollars each; can be obtained as rewards for working alongside Concupi members, or found in the field.

10: Technisphere.
Coloration: Silver with green lights across the entire surface, glowing green trigger button.
Usage:A modified Premier Ball that has been hacked with Team Technica technology. Hacking into the Technica systems as a basis, the ball is actually able to draw from a portable PC up-link in your average Pokédex device to actually cycle Pokémon into the field without ever having to switch balls. It is also capable of capturing Pokémon without wasting a ball, as the device is held, not thrown, and the capture beam is fired from the device at range. The main benefit of this type of ball is obvious: It won't break or be lost when thrown, and you only need to carry one. The Technisphere is also required to steal Team Technica Pokémon and liberate them from their cybernetic brainwashing, though there is no way to reverse the permanent physical changes.
Cost: Not available for sale; uniquely crafted and only available if one can capture a Team Technica capture device for the Triple P to study. Cost of research and reverse-engineering may vary.

11: Prime Ball.
Coloration: Silver with a gold trigger switch, no other features normally. Seamless at first examination. Prime balls are often numbered or bear a special marking to indicate their association to a tournament or event, and are frequently limited run items.
Usage: Prime Balls are a regional take on the Premiere Ball, specially available during tournaments and special festivals. They are rather expensive and rare, but oddly are no better than a Great Ball. They are essentially a sign of attendance to events and special involvement.
Cost: 800 Poké dollars for a pack of three at certain events, though they can also be obtained as part of special festivals and Pokémon capture events, such as regional Expeditions.

12: Élite Ball.
Coloration: Platinum with solid gold inlays and diamond trim. Fine detailing in gold, trigger button is crystalline and glows white.
Usage: Élite Balls are the top tier of disgustingly luxurious, overly expensive ball. Luxury Balls are well below the cost level, and also weaker in general strength. Owned only by the very rich and those who have less sense than money, they're purely a status symbol. They are roughly the same strength as an Ultra Ball, which is the least one can ask for the cost. They also greatly improve the mood and loyalty of any captured Pokémon, while providing the additional benefit of healing Pokémon statically while they are being transferred from storage to the ball and vice versa. Effectively, they tap directly into Pokémon medical facilities without having to go to either a hospital or a Poké Center.
Cost: A ridiculous 2500 Poké Dollars for a single ball.

13: Stun Ball.
Coloration: Clear plastic cap and white lower shell. Yellow trigger light.
Usage: This is an odd duck, in that it's for the exact opposite purpose of normal Poké balls. These special balls are actually NOT standard, as they do not have a teleportation matrix. Instead, they are intended to be thrown at an aggressive Pokémon as a means of escape or diversion. The clear top allows high-powered lights to rapidly and repeatedly flash, blinding and disorienting dangerous creatures so a Trainer can retreat. These are considered standard survival gear for wilderness travel.
Cost: Cheap at 200 Poké Dollars for a five pack.

14: Phase Ball.
Coloration: Flickering translucent cap that shifts through purple, blue and green. Same colors flash on the trigger button; black bottom.
Usage: Phase Balls are an especially unusual device; they are based on research of the teleporting abilities of some Pokémon, such as Abra. The ball, when thrown at a Pokémon, actually teleports behind Pokémon while maintaining momentum. It changes direction, however, allowing a Trainer to throw a ball at a Pokémon from behind, catching it off guard. The biggest problem with these balls is that they sometimes go haywire, especially in enclosed spaces, and instead teleport in a random direction. It's roughly a one-in-six chance, which is troublesome given the cost.
Cost: An above-average 450 Poké Dollars a piece.

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Of special note:

The Crystalis Array, a non-ball related capture system used by Team Technica, can be used to steal Pokémon from trainers. It's effectively a high-tech electronic rig, normally connected via a glove to a circuitry equipped belt. It acts as a portable means to break the encoding on owned balls and steal the Pokémon inside, as well as a ranged capture system that is a simple point and fire interface. Highly advanced, it removes both the limitation of physical projectiles and the six Pokémon limit. In fact, Team Technica can pull Pokémon from a collective pool across their network rather than having to select their own Pokémon.

The Heart of Ōshū is a possibly mythical piece of ancient technology associated with a lost civilization that supposedly ruled as an empire across Ōshū a thousand years ago. The technology behind it is well beyond the capabilities of any known ancient civilizations, involving complex clockwork and a prototypical capture field generated by irradiated crystals. It's said that it could be used to capture any living Pokémon, even more powerful than the Silph. Co Master Ball, but more importantly the legend claims there is already something contained within it, an ancient evil that was brought to heel to protect the world, and in doing so doomed the ancient Ōshū civilization. The current whereabouts of the Heart of Ōshū? Unknown.

The Mystery Ball is a strange, somewhat organic device of unknown origin found in the wilderness of Opoc. The balls are only found in loose clusters in deposits outlying the centuries old Stranny Voronka crater. Originally thought to be some kind of odd stone, the grey-green balls are soft to the touch, strangely warm, and when opened reveal what appears to be a plant-like interior with the basic outline and components of what appears to be common Poké Ball components. Experimentation has proven that they can function as Poké Balls, but the Pokémon captured with them invariably come back out...Stranger.

I love everything about this.

Whuts the deal with human x pokemon breeding.

Like how many humans are "compatible"?

Is it a known thing???

For the simple matter of Pokephilia, it seems to be a semi-rare thing. There are communities that are involved with it, obviously, but it's not as common as it might seem. There's a historical basis for it, of course.

As for actual crossbreeding? It appears to have some vague connections to the theory that all life on Earth, or at least that iteration of Earth, stems from the same genetic source. Humans are, after a fashion, just another offshoot of Pokemon. As it stands, that certainly explains why some are actually biologically compatible for the sake of breeding.

But is it common or well known? No. A handful of confirmed biologically malleable surrogates have been found, and there are probably many more. It's just a matter of luck and personal proclivity to figure it out.