It looks like you have an eye on a house that's currently in the foreclosure process. Typically there is a six month redemption period after the sheriffâ€™s sale. After that, it will most likely take 2-3 mos after the redemption deadline for the bank to put it on the market. Regarding your second question, I'm not aware of any way to purchase the house from the bank before it's been listed for sale. To my knowledge, banks don't sell homes directly to the public. First of all they don't know what the market value is until they receive a BPO (Broker's Price Opinion) and also each state has different laws and requirements to sell a house. Therefore, they will sell it through a real estate broker and possibly work through a third party that handles these types of homes as well. Unfortunately, if you aren't able to buy the home before the sheriffâ€™s sale, I don't see that you'll have a chance until it comes back on the market again.
If you're really interested in one particular house, I would absolutely make sure that you've spoken to a lender and done all the necessary pre-approvals. I would also have a Realtor with experience in bank mediated transactions ready to go so you can be the first one to make an offer. I'm seeing the trend lately that banks will deeply discount the homes so as to draw a lot of interest. This often results in multiple offers that drive the price up over the listing price and will sell very quickly. If you're truly serious about buying that particular house, it's not the time to play any games or put in a low bid.
I hope this helps. Good luck!