In the U.S., a federal act - the Protecting Tenants at Foreclosure Act - requires banks on federally related mortgages to give a 90 day notice to quit. You can assume that the mortgage is federally related. After that, in most states, they have to go to court and prosecute an eviction.
Renters make a lease agreement with a landlord.
If he lost his renters privilege, he is no longer a landlord
The Landlord
If it is foreclosed then he does not own it. You cannot rent a property that you do not own.
No
No, landlord insurance does not provide protection to the renter. Landlord insurance simply covers the landlord if an issue that is of their fault arises. All other issues are at the renter's responsibility. All renters should acquire renters insurance.
From what I understand they have to move immediately .
no
No. Signed is signed.
Yes.
Is called a lease.
As long as your landlord has control of the property he still has the right to collect rent: whether the house is foreclosed is between your Landlord and his mortgage lender. If the property is taken over by the mortgage lender they may ask you to leave. There may be some form of protection available for you, the Tenant, before you are forced to leave. Get legal assistance as soon as you learn about the foreclosure so that you can be prepared for what's next. You may or may not be required to leave soon.