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.
You may want to ask yourself, which option are you most comfortable with? Not everyone is suited for being a long distance landlord. There is however the option of having a property management company oversee and handle the leasing for you.
An appropriate person to ask would be your accountant. Gather all the figures needed and evaluate which option will be suit you financially.