Never, unless it is expressly written in your lease agreement.
They are $2 apiece. If I were your landlord and you asked me that I would turn it off.
Normally an air conditioner is controlled by the tenant as part of his electricity.
The landlord, because he/she owns the property.
I don't know Arizona laws specifically but ... I expect the law will say if the property had working air conditioning when you signed the lease and moved in, then it is the obligation of the landlord to maintain it in working condition.
You would need to read you lease but in most cases the Landlord is responsible for the maintainance of air conditioning units
Only when you don't turn it on.
There are many reasons why an air conditioning compressor might not turn off. There is likely a wire that is not connected properly.
A manual air conditioning system is one where you can turn it off and on when you want and control the temperature at which it is set.
Nothing Air Conditioning is a luxury, it is not needed for essential living
No. While in air conditioning mode, the air will assist in the dehumidification.
I don't know of a state that requires a landlord to provide air conditioning. I'm in Massachusetts, which, like most states has laws about heat, but not A/C. So, this wouldn't violate any sanitary code. It might be a breach of contract, but, then, if you didn't pay your rent, that goes both ways.
Stuck compressor contactor.