Does Private Mortgage Insurance cover foreclosed homes?

Questions on foreclosed homes

1) If PMI insurance does not cover the deficiency amount owed on the home then does the bank sell the property for the deficiency amount owed, or the asset value of the house and property?

2) Are there any website/places someone can go to bid on a house without other mortgage brokers or realtors bidding on it too?

3). If there is only $20,000left owed on a house and that’s the only amount the bank is losing why not sell the house as is but maybe add on another 5 or 10 thousand dollars to the closing cost for the bank to still make a profit.

4). When the banks pay someone to fix up a house before selling it, do they shop around for competitive estimates for repairs or check behind the contractors to see if the work is done correctly and to code ?

5). If a bank knows they do not want to sell a house for no less than $50,000 at an action then why does the bank not have the starting bidding closer to 50,000 instead of $10,000?