To answer a couple of your questions:
2) I don't know how difficult it is for someone going ROTC/OTS to get an AFIT slot right after college. I do know that at USAFA, we had about 20-25 slots. At the time, I was able to go to a civilian institution (sponsored by AFIT), kept my projected AFSC (92T0), and still went to the same UPT base I had selected originally. Talking to a more recent graduate, they no longer keep the base you chose, but you will still keep your projected AFSC...that is, unless you go non-PQ, etc. If you are a non-rated type, then you were probably already on the road to a 62 type AFSC and so it's a moot point. If not, then unless you washout of UPT/UNT, you're safe from the engineering field.
3) The only official guidance is that you must possess a BS vice BA. I would imagine a Master's of Engineering would be a beneficial thing in your records.