It can cause this problem since you will have to work the engine much harder to get the power needed and the exhaust can not get out. If you are talking about water temperature being too high, not really. Check for a sticking thermostat on this one. More often it will cause a loss of power and if it has a carbarator it can cause spit back out of the air cleaner.
Not likely but possible.
It could, yes.
Yes, it can if faulty or missing.
Depending on the cause of the misfire, it could damage the catalytic converter.
It is one of many possibilities.
It is illegal and will cause the vehicle to pollute the atmosphere.
No, very doubtful.
Engine mounts
Yes if it is totally clogged.
Yes, a catalytic converter can cause a vehicle to vibrate and stall. It will do this when it gets plugged because it causes the fuel mix to be disturbed.
catalytic converter
Yes, a bad cat can cause issues.