As to the foreclosure: leases dated after the landlord's date of default (its failure to make the mortgage payment), can be terminated in the foreclosure action. Having said that, the foreclosing bank must notify you of the impending foreclosure; and if successful in the foreclosure action, must commence an action in landlord-tenant court to evict you. These steps take several months, if not more, to complete. Keep in mind that landlord's (or their successors in interests, such as foreclosing banks) can not evict tenants. Only a sheriff's officer holding a docketed judgment can evict a tenant. Your legal position greatly depends on the timing of the lease execution relative to the timing of the event of mortgage default. I recommend you bring your lease to a real estate attorney for a review of your situation.
There's no need for me to comment on the HVAC system as the previous answers cover that topic.
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A few things:
Your landlord is responsible for maintaining the HVAC system, generally speaking. Regardless, the system is broken BEFORE you moved in - that cannot be charged to you under any theory. Fix or replace, it matters not - whatever gets the job done and costs less is 'commercially reasonable.'
As for the foreclosure, your lease will survive foreclosure. You should, however, find out who the foreclosing mortgagee is and send them and your LL a letter (via certified mail, return receipt requested to both) indicating you are aware of the pending foreclosure, are an affected 3rd party, and want to be kept in the loop to the extent you are paying the proper party monthly rent. I'd also suggest photocopying every check you send to the LL and sending it certified mail, return receipt requested) and keeping copies of all paperwork. Alternatively, you could open up a bank account and escrow the rent until the matter is resolved, but you'll be looking at an eviction hearing (which you can win by simply paying rent.)
You probably cannot break the lease at this point, since your LL must be given a reasonable opportunity to cure the problem - he's got over a month. If the AC unit is still not working on 7/20, then you might be in a position to breach the lease.
The foregoing is not legal advice, and nothing in the foregoing shall be deemed to create an attorney client relationship. If you feel you need to speak with an attorney regarding your issue, it is recommended that you contact an attorney with expertise in your area of inquiry. The information related above is purely for informational purposes, and should not be acted upon without speaking with qualified counsel familiar with you specific situation and the laws related thereto.
If the HVAC works, it does not matter whether it was fixed or replaced. Your landlord is responsible for that, unless the lease states that you are responsible for it.
Since it was broken before you moved in, you should ask it be fixed before you move in.