The primary obligation of the landlord is to be responsible for the maintenance of the premises, regardless of the disposition of the tenant. The tenant is legally obligated to allow entry for maintenance and repairs with a twenty-four (24) hour advance written notice of entry by the property owner.
Issue a notice of violation for the tenant’s failure to pay rent. The failure to pay rent in full is irrelevant to the ongoing maintenance. Maintenance of the roof and windows is hardly an issue related to habitability, and does not constitute a legal reason to withhold rent without the permission of a court.
Issue a notice of violation for the tenant’s unauthorized change of locks without landlord consent. The landlord is legally allowed to replace the unauthorized locks and provide the tenant with a new key set, even charging for the lock replacement.
The new appliances should not be installed until the tenant has either vacated the premises, or has agreed and made full monthly rent payment, in accordance with the new LPA Lease Agreement (which surely you are using). It is sometimes difficult to get the full cooperation of a resistant tenant to new management -- this is the reason property owner’s evict prior to purchase or soon after purchase. Judgment call … but, in my opinion, the rent should be increased to full market value, if the tenant agrees and remains be prepared to evict at the first sign of the next violation.