A lot depends on the bank. If it's a local bank you will typically hear back faster then you would a national bank. Bank owned usually have a quicker turn around time then a Short sale listing as well.
If there are several offers, I am sure the bank will ask for best & highest. It does take some time for the bank to crunch the numbers. They usually have a base number they have to get and work from there.
I hope it goes well for you.
What will most likely happen next, and it can take 3-5 work days (banks don't function on weekends) is that you will get a request for Highest and Best offer. This means the bank is rejecting all offers and saying to everyone to come back with your best offer and they will pick one. Unless there is someone that came in above listed price, and has no objectable terms in their offer, the bank will usually ask for highest and best. If someone came in over list, they might get the approval. You should hear something in a few days, banks are slow.
The way to find out if a bank has a home is to go to your county assessor website and do a property search on the address. It will list the owner of the property somewhere on that page. Best wishes.