Silver or brass coin?

Bottom left has the appearance of silver, but I have a few bronze coins from roman times that are actually tinned bronze.

Both bronze, but at one time they would have had a very thin layer of silver over the base metal, to appear silver. It wore off very quickly though, and you rarely see coins of this sort that have more than a trace of silver left. Both these two coins are rare enough as it is. They would have cost at least a couple of hundred dollars each if there had been much silver remaining.

The coins you have would not have been "tinned." If they are what I think they are, they would be late 3rd century "Antoninianii" that are bronze, like these, but had been coated with silver when new.

Were those coins always that rough and jagged around the edges because of lack of minting technology? Or is this due to the ravages of time?

Most often the irregularities are due to the primitive way coins were struck. The metal squeezed out between the upper and lower dies, producing odd shapes. Now and then, one came out pretty much circular, but judging from surviving coins it was fairly rare to do so. Other flaws include weak areas on one side or another, from uneven striking, cracks, and even missing letters in the inscription (when some bit of dirt or metal from an earlier strike has stuck in the die.

Today, we have a sort of collar that the dies fit into, that prevents the metal from squeezing out from between them.

However, sometimes coins were clipped -- someone has snipped a thin slice from the edge. If that's done on enough coins, you end up with enough silver to make new coins. In the Byzantine empire, the government itself often called in old coins, snipped their edges for the bronze, and struck new, bronze coins from the trimmings. But, most often it was illegal. In modern times we add raised rims, serate the edges or even strick inscriptions around the rim to prevent clipping.