Where exactly is "rural Phoenix"? If you are not already working with an REO-experienced Buyer's Agent, I would strongly recommend that you find one. Most of the questions you've asked are the types of questions that can make or break an offer, REO or otherwise. And consulting with your own Realtor is the best way to get your answers. The answers are also property specific, in that there is no set amount that you offer on a bank owned property ~ sometimes higher than list, sometimes lower.
Let me know if I can help.