No

Unless you have return ducts in every single room (and very few houses have that).

Another way out, is to have doors with vents (like they used to have on older ships); this allows the air to flow out of the room "as if" the door had been left open.

Generally no.  If you want to close the door or do only one room, consider getting independent window units or mini-split A/C.

no. needs airflow 

Normally in a commercial building the air is balanced by--hopefully--qualified technicians. Since most home owners have neither the expertise of the knowledge to balance the air, there's no yes or no answer to your particular situation.

Each room in the house should have an independent in vent and cold air return 

The term cold air return is based on the vents being used for heating 

Since the central air uses the same vents that would mean all rooms would 

Taken care of the problem is where is the thermostat 

If it's in the living room the other rooms may be colder

no, as a rule, but if there is a gap under the door and the room is small, it's OK

there is only one return duct, and the air has to get there from the various rooms to the one with the return duct.

No, you want the air to flow into the unit and back into the roos

No, i like air circulation 

Central air works by pushing air to each room which then must make it to the return air register. So it works most efficiently with the doors open.

Answer:

No, you should NOT close the doors of all the rooms. Do the opposite.

No