The foreclosure or nonpayment of the mortgage by the landlord does not relieve you of the obligation to pay the rent. Essentially you got what you bargained for - the right to live in the property and as long as you have that - the rent obligation is intact. The foreclosure process timeline is dependent on a lot of factors - the most important of which is whether the homeowner fights it. That can extend a timeline substantially over an uncontested foreclosure.
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As long as your landlord is still the owner of record, you have to continue paying rent. Whether the landlord has been paying the bank is irrelevant to your legal obligation to pay rent.
If the house is actually foreclosed upon, your normally would have 90 days to vacate. See:
The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author (who is only admitted to practice law in the State of California). For specific advice about your particular situation, consult your own attorney.
To answer the first part of your question, you can always check with the County Recorder's Office to determine whether the house is indeed in foreclosure.
Please note, even if the owner has not paid for the mortgage for 6 months or more does not mean that the foreclosure process has started (lender serves Notice of Default on borrwer).