In California (and probably many other jurisdictions), the landlord has a right to enter without notice for emergency issues such as a burst pipe. Checking for rodent activity does not sound like it rises to the level of an emergency. So under normal circumstances, they must give 24 hours' written notice and only enter during "normal business hours" which is usually interpreted as Monday-Friday, 8AM-5PM.
if a landlord bugs my apartment, is that an invasion of privacy?
A tenant ANYWHERE can be told to clean their apartment ! The tenant is only there 'at the grace of the property owner' - and pays for the use of the accommodation. It is not unreasonable for a landlord to insist the tenant keeps the property in a reasonable state of cleanliness !
The landlord
Visit the apartment or contact the landlord.
Usually the landlord, but there's no law about it.
If you have a lease your landlord would have to take you to court to have you kicked out of the apartment. If you are a month to month tenant then the landlord can request that you vacate with 30 days notice.
You can usually tell by the upkeep of the apartment building. As far as your landlord's character try talking to some of the other tenants.
Follow the landlord's proper procedures for requesting such transfer. There may be a waiting list for that apartment.
Protect your rights as a landlord or renter: use a rental or lease agreement to outline renter and landlord responsibilities for apartment maintenance.Click here to fill out the Apartment Maintenance Responsibilitiesform
What a landlord verifies is completely up to the landlord
That depends on the landlord.
The possessive forms are landlord's and tenant's; for example:The tenant's apartment is the best one in the landlord's building.