If you are paying rent then you are tenat and subject to and protectd by tenanncy laws. The specific laws vary widely by region, but in general if you have currently paid your rent in full you can remain in resedence; unless the landlord has other cause to evict you.
Yes you can
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.
When the bank foreclosed on the house, they took it back. Now it's time to move out.
I would think so. Though the bank should be using all means possible to get that cash from you to pay for your currently foreclosed house. Even if they don't, paying in full with cash for anything will always be accepted.
No, I can't
If it is not specified in the contract then it is likely at the descretion of the lender.
If both names are still on the loan, it effects both people.
The foreclosure will affect your credit record. You are fully responsible for paying the loan.
The bank does not care who holds the mortgage. If the loan is not being paid, it can be foreclosed on.
You can contact the lender or lien holder who foreclosed on the property and make your offer to them.
No the bank owns the house.
The landlord can correct the problems for which the house can be potentially condemned. But the landlord cannot evict the tenant just for saying that.