Legal Question in Real Estate Law in California

First off, if you have a lease, they cannot order you out until the end of the lease, or for 90 days from the sale, which ever is longer. If you are month-to-month, they have to give you 90-days from the sale. During that time, however, you must "attorn" to your new landlord. That's an old fashioned word meaning you must treat your new landlord in every respect as you were obligated to treat the former owner. That means complying with all terms of the lease or rental agreement with the old landlord, or if no agreement, then complying with the law of tenancy. That will always include paying the rent when due. If you fail to pay rent or otherwise comply with the rental agreement or lease, you lose the protections of the 90-days legislation, and they can evict you just as if they were the original landlord and no foreclosure took place.

Yes, you have to pay rent for as long as you are in possession of the property.