So like when it says +2 to a certain skill, it's just adding to that skill without actually showing up? 
 
Or is my game glitched? Because When I add a mod the bonus skill points aren't showing up on my skill tree.

I'm pretty sure it just adds it without adding a stat to the skill page.

 Seriously?! I find that rather lame.

Can a class mod bring you above 5/5 on a skill as well?

yes you can get above 5/5 it doesn't show on your skill page but just consider it as two more points with the same benifits

yes, you have to be shooting corrosive damage for that to work.

Another question, will the skill bonus apply without you having some of that skill, or the skill tree requirements?

From what I've been experiencing you have to have at least one point in the skill to get the mod to add anymore to that skill.  Gearbox really should add more tooltips to the skill tree screen that reflect the current mod you have in.

Another question. When a class mod says something like +40% team accuraccy, does this apply to yourself as well? Or just the team?

I think this game really needs an FAQ since a lot of things seem a little blurry.

" Another question. When a class mod says something like +40% team accuraccy, does this apply to yourself as well? Or just the team? "