No.
A bad water pump can cause your car to stall if the bearing has failed or it is causing overheating. A seized bearing will put excessive strain on the engine and stall it out.
Yes. It does big time
no
Yes, the signal to the PCM can be wrongfully perceived as low coolant, even if the car is full of anti-freeze.
A bad spark plug or spark plug wire will cause your car to run rough. A dirty air filter will also cause your car to run rough.
A fuel pump relay switch can cause your car to stall after starting. A malfunctioning fuel pump relay switch can cause your car to not start at all.
possibly the coolant temp. sensor
yes it will
Vaccum leaks
timing is wrong, coolant leak, bad radiator or thermostat, head gasket....
No, it will just make the car loud.
Possibly the Head Gasket is blown.