In my area, once the foreclosure occurs, the new owner does not have to honor the lease. An exception might be if the lease was recorded in the land records and had priority over the mortgage being foreclosed, but I’ve never seen this.
I’m not knowledgeable about Colorado law but in the states I’ve invested in, the lease remains in full force and effect until the foreclosure sale wipes it out, unless it’s one of those rare cases where the lease is senior to the foreclosing parties’ lien.
If your the tenant, I definitely wouldn’t be giving the landlord any more money, especially if he is already holding a security deposit.
That’s a tough one. Normally the lease belongs to the property, so even if ownership changes, the new owner has to honor the terms of the lease. But if the tenant abandoned the property, the question would be - who would pay to do anything about it?