Fuckin' A means: 'Absolutely'. Or 'Damn straight'. To make the same statement, Aussies say "Bloody Oath" (or maybe 'kern Oath' if my sources are correct). There is no need to parse it to try to figure out what the 'A' means. It just is. All this 'awesome' and 'can be either positive or negative' comment is crap.

Short for "fucking awesome." Usually a way of strongly saying "you're right!," but can also be used as an expletive if annoyed.

An affirmation spoken with religious zeal and enthusiasm.

yes; to agree with someone.

Thats right, That really hurt,
Thats too bad, Thats great.
You can use it as feed back for pretty much anything you need. It all depends on the way you express it, and want it to come across.

A way of saying, "Indeed," only less queer.

Fucking Amen, as in agreement with a statement. However, the speaker will not say the Amen part fully as not to blaspheme against God. Stupid teenagers will someones use it in a derogatory sense as a way of saying "fucking asshole" but teenagers are stupid as hell.