1) Can I train my battle bunny to have extra attacks? What if I give it the appropriate nekote (ninja claws) and ear blades?
If the GM lets you yes. As soon as you give it weapons though, they are not natural attacks
2) Does making multiple attacks lessen damage? Are there feats like 'focus chi' that let you forfiet attacks per round to increase your damage?
No on both counts - the former because we've never done that and the second because we have Power Attack and Bullseye
3) Presuming there's an astral or spirit combat, are there feats that let you strike extra times in those mental/spiritual conflicts?
We are not covering astral combat in this book.
4) Extra attacks sound cool, can we also use feats for bonus spells, or special abilities?
ABSOLUTELY not. This benefit applies only to natural attacks. There are feats that let you cast multiple spells in a round, and other feats that let you use non-natural attacks multiple times in a round, but this feature was designed specifically for handling ingrained, organic weaponry.
5) What about things such as two strikes at the same time? Yes, less damage, but harder to parry.
There is a trick called Whirling Strike that will probably handle this, but maybe not in the way you're imagining.
6) I had more annoying questions, but it's too late to remember all of them.
Oh, that's enough for now