For a humorous take on this check out this YouTube video:

http://www.youtube.com/watch?v=SM7oWKgCVo4

I assume you mean REO's that are listed in the MLS.

1) In the realtor's comments sections they usually have comments relating to how to submit an offer.

2) Generally that involves a separate pre-approval from  their chosen bank. (you don't have to get a loan through them, they just want to know the nitty gritty of you being able to close, and have the opportunity to sell you a loan)

3) Generally, once they have an offer, they accept offers for a set period of time, and then review all offers to pick the winner and a back-up or two.

Some banks will do subsidies, some won't. Some will allow inspection contingencies, some won't. If you know you like one in particular, and what the close date for offers is, I recommend paying for an inspection before putting in the offer.