Can a landlord use your last month's rent to repair the apartment?

No. Your last month's rent is that: your last month's rent. The landlord must allow you to stay in your apartment for the last month and not use that money for any other reason. If the landlord collected a security deposit then he can use it to repair his unit: IF you are the one who damaged it outside the realm of normal wear and tear. He cannot use your security deposit as your last month's rent unless you agree to it.