I would hope that they simply save a hash of the fingerprint with a reasonable level of collision built in to make it difficult to tie a hash to a single person's fingerprint (maybe ~10 people would have that hash?). I would imagine they could then use some sort of secret tied to the device id and hash pair to positively identify to the server.
1)They said the detection gets better every time you use it. So my guess would be that multiple versions of the raw fingerprint data are stored inside the A7 chip. (That information never leaves the chip.)
2) You can use your fingerprint to authenticate apps like iTunes, as well as third party apps. For this, yes I am sure they will use some hash that cannot rebuild the fingerprint.
edit for clarity