Yes. They need to give you a specific day and time.
At least 24 hours.
The lease probably says that the painting must be done in a "workmanlike manner." It is their property, so as long as they give you advance notice they can come in and inspect it.
In America, no it is not. The landlord is only allowed to enter your appartment with your permission, or in the event of an emergency (broken water line, fire, etc.). The landlord has the right to inspect the dwelling, or show it for resale, but you're legally entitled to reschedule if the timing is inconvenient. You do, however, have to respond promptly to a request to inspect or show (48 hours is considered acceptable). The events your question describes are trespass.
Yes. The co-signer should be able to inspect the premises she/he has taken financial responsibility for.
In almost any state a landlord can enter the premises if there is good cause (leaking pipes, electrical problems, etc;) Your landlord should make an effort to contact you first but regardless of your consent, the landlord may go in and inspect if there is a potential hazard to the building or other tenants. It is important to remember that while your landlord owns the property, you, as a renter retain temporal eminence (meaning that you are the temporary owner). However, the landlord has a right to look after his/her long term interests. If the landlord feels that you have violated the terms of the lease, let's say that your contract forbids a water bed in the apartment unit and your neighbor below is complaining of water leaking through the ceiling; the landlord attempts to contact you by phone but you do not answer. In this case the landlord has the obligation to the one tenant complaining of water leaking through the ceiling by entering your apartment to find the cause. Like most legal matters the situation is governed by the "reasonable-ness" of the case. Your landlord cannot enter your apartment to look around, to open your drawers or inspect the quality of your furniture or even to make sure you are in compliance of the terms of the lease, that would be a violation of your right of privacy. It would be reasonable to presume that if your lease stated that you may not have a dog as a pet for any period of time and the landlord hears barking in your apartment, he /she may enter because the barking would make it reasonable to believe that there is a dog in the apartment.
Before you get a lawyer go to the city and get them to inspect/ fine the landlord. You can file a complaint and they will force the landlord to clean it up. Let the city handle it and it won't cost you anything. Plus, he may have to do more than you see or may have had pass complaints against him.
A building inspector inspects buildings in order to make sure that they are safe to be inhabited. Some building inspectors inspect buildings for people planning to buy whereas other inspect them for people planning to rent, or the landlord renting the property.
If you want to get your cleaning deposit back, clean everything thoroughly, including the carpet, and make sure the landlord knows so he or she can inspect it.
I/you/we/they inspect. He/she/it inspects.
The future tense of inspect is will inspect.
If you are on the Housing Choice Voucher Program (also known as Section 8), he can call his Housing Program Coordinator (HPC) for help. The HPC can inspect the home and if it doesn't meet federal housing quality standards (HQS) the hPC can order the landlord to fix the problem or help you located another home to move into. If not then you can call the Code Enforcement bureau of your city or county and they can inspect the home and fine the landlord or condemn the home.
Inspect in French is "inspecter."