So you are looking to wholesale?
First off with an REO property they do not allow wholesales. So you need to figure out a different way to state the buyer. Meaning you might use an LLC. 123 Main Street, LLC. That would be the buyer. Then if your offer is accepted you will form that LLC and sell the actual LLC to the end buyer.
Another method is to use a land trust.
Another method is to do a double close. Most title companies will have no idea what you are talking about. This one is much harder.
The last method is to purchase the house yourself in your name or your company name and then sell it at a later date to your end buyer. I have done this method 3 times. It does cost you more in fees though then those other 3.
As far as the ratio of accepted/offered. I don't know what my ratio is. I know I study the deals very closely before I waste my time making an offer. For example lets say a house just came on the market at 150k. This house has a ARV of 180k. It needs 20k in repairs and I feel if I can get it for 120k it would allow my numbers to work. I wouldn't even waste my time offering on this house. It is just too fresh on the market and the bank would never go for it.
Lets change the numbers around though. 180k ARV. Listing started at 175k and over the next 6 months has been lowered down to 150k. Now I think you have a slim chance of getting this for 120k and I would in fact consider making an offer. The bank has tested the waters for 6 months at this point. They are starting to think 120k might be a fair price.
Looking back I bet my ratio is very very high on what I have gotten accepted. I would think it is possibly as high as 30-40%. Like I said though I don't make stupid offers that are a waste of everyone's time.
Another thing to consider is look around at who the listing agents are for the REO's. If you study for a while you will start to notice only a handful of agents handle all the REO's in your area. One of the best things you can do in real estate is form relationships with these people. The way you form relationships with these people is buy houses. Once they see that you are a serious buyer, you close when you say you are going to close, you don't default on your commitment I promise more of your offers will get accepted. Piss these people off with annoyingly lowball offers all day long and I doubt you will go far.