Does the time of year that you apply to a job matter? Should I be searching for jobs at certain times more than others in general?

Yes and no. Some industries follow graduations looking to hire entry-level. Others will have layoffs at the end of some financial quarters (Q3&4 especially).
Generally, the further the job is from entry-level the less likely the hiring follows to a cycle.

Question: How can i improve my chances of getting hired after being layed off.

And will being fired for certain reasons hurt my chances ?

Be direct with your interviewer that you were laid off. Heck, I included that on my electronic resume submission (not paper) when I was in that situation.

99.9% of the time the reasons for a firing will not be shared externally due to legal liability.

Can you elaborate on the legal liability?

The company does not want to invite a discrimination or defamation lawsuit because of saying harmful things about you.
NOTE: This assumes USA. I cannot comment on how it works in other countries.

Oh thats interesting to know, thanks.

👍

does volunteer work count toward a resume if it's relevant to the field one is entering?
EX: Exotic pet care when entering a zoo as a place of work.

💯 yes if you volunteer consistently, though it will not be regarded as highly as work experience.
Make sure you clearly label it as volunteer, the time span of involvement, and how often you volunteer (i.e., hr per week/month).
Where you place it depends on many things...

I'm actually searching for an NSFW porter who can port SFM / blender models to Gmod playermodels as a hobby.
I paid a comissioner $40 USD in steam cards and he just ghosted me saying he couldn't accept the money... Lost 2 precious codes that day ;-; All cause he said his computer "couldn't accept that currency"... I felt betrayed and ripped off at the same time.
So yeah, searching for hobbyists from now on...