The air conditioner unit in the house is damaged, does the landlord have th right to give me a notice o leave the hous in 30 days.

Once a lease expires, and the landlord does not require you to move, the lease is now converted to a month-by-month lease.  So if your lease expired, and you have continued living there, his right to have you move has nothing to do with the air conditioning, at the end of the month, you can be asked to leave.