if you have mold coverage, yes.
To the black wire on the fixture.
The wall and ceiling textures do not have to match. depending on your taste, the ceiling could be popcorned or swirled, or the walls could even be an adobe style. The homeowners imagination is the only limit.
Black to Black - Black from the ceiling is a hot wire and should be switched Red to Blue - Red wire is another hot wire and should also be switched White to White - White from the ceiling is the neutral and should not be switched. Your wall should have two switches, one will control the red wire, one will control the black wire. If you wire your fan as above, one switch will turn the fan on, the other will turn the light of the fan on.
The answer to this question has little to do with the cracked ceiling but what caused the ceiling to crack in the first place. If it is caused by settling of the home or earth movement then the ceiling crack would not be covered. If a tree limb fell due to a windstorm and damaged the ceiling then it would be covered under a homeowners policy.
The start capacitor in the fan motor needs replacing.
See: "How can you re-wire a wall switch that controls an outlet to control a ceiling fan?" (Follow the link below.) The procedure is the same whether the new device is a light fixture or a ceiling fan.
I presume you mean 'homeowner's insurance'. Some contracts do cover it, some don't. You will have to look at the small print in your own policy.
You'll have to refer to your policy language or consult with your agent. Most homeowners Insurance policies offered since the late 1990's automatically exclude coverage for mold or fungi and relegates back to a home maintenance issue. Also note the pre-existing conditions clause in your Home policy. The home Warranty purchased with most homes new and used, warrant property condition at the time of delivery.
It depends on what caused the leak. If your leak was caused by a covered peril on your policy such as Hail wind fire etc, then your homeowners insurance would cover the cost of a repair and the repair of internal damage resulting from the leak. If the leak is resultant of aged material or normal wear and tear such as an old roof that has outlived the life of the material, then that is a maintenance issue and ceiling damage will continue to occur every time it rains. Your insurance company would probably fix your ceiling but not until after you replace the aged roof.
If the ceiling fan has a light fixture included in the fan, then there will be three. A white, black and blue. The blue is for the fan if the owner wants the fixture to be switched individually from the fan. Other wise there are only two wires to connect to the fan, a black and white.
The roof likely wont be covered for 'leaking' unless there is 'covered' damage to it (such as wind damage). The interior damage may or may not be covered depending on your specific policy. See Section I- Perils Insured Against, Coverage A (building) and Coverage B (other structures) in your policy. //