what are the precise steps in finding reason(s) why 2.7L Avenger is overheating

First thing I'm going to ask is when was the last time your cooling system was serviced? A clogged system could result in overheating. Thermostat could be stuck closed not allowing flow through the radiator once up to temperature. Radiator could be plugged. Do you have heat in the car? Is there pressure in the system when it's up to temp? Simple check would be to squeeze the hose going to the top of the radiator. If you can squeeze it easily and there is no pressure when up to temp, you have a plugged system. Just a reminder, if you're going to add water, make sure it's a 50/50 mix with antifreeze coolant.

My dodge avenger 2008 overheated and went off on its own does this mean that the engine is burned or does it go off automatically and stops the engine from burning

Make sure the cooling fan is coming on when the car gets hot. The engine will not automatically shut off when it over heats unless you seize the engine.