REO docs include the 1 contingency your looking for as the bank will override the original contract with an addendum that grants you a 10 day option without a fee. you can submit as low as a EM as you like but if your planning on closing why not get their attention with a nice EM. Regardless of the amount, be sure to include a copy of the EM check made out to "title company", its part of the package (contract, copy of EM, bank statement/proof of funds).
The agents who list REO's, are who i refer to when I say REO brokers. I would say to use a buyers agent to submit your offers. As a buyer, I have never had to back out of a contract and I feel this had gained my offers and b-agent favor with certain brokers as it seems my offers keep getting accepted by the same set of brokers.
If you plan to close cash, and you are serious about wanting to buy, then use your buying power to get offers accepted. Beware not to burn you or your agents rep by not closing deals especially with big brokers.
Its good your out there trying and asking questions!