A loose engine mount would not normally cause the engine to fall out because each car has several motor mounts. A loose mount could cause the motor to be off of balance.
a loose or slipping belt
Not usually. If the rocker arms are loose because the cam lobes are worn down, that could be an indication of a worn engine, which might have bad rings or loose valve guides, which would cause an engine to smoke.
Yes, a loose distributor can rotate so that the ignition timing for the engine is lost.
A loose wire would cause the horn to stop working on your Dodge Avenger 2.4L engine.
Only if you run it out of oil. Otherwise no.
It could be a loose radiator grill, license plate holder or similar. It could be a loose cap in the engine compartment or even a problem with the engine.
check for a loose or broken vacume line on the engine probably on the intake
The bracket that mounts the carburetor to the intake split in half. It has been repaired.
Hard starting, corrosion at terminals, eventually cause a weak charge on the battery from cranking too much, will not start at all, can cause your carburetor to flood.
There could be loose rings in the engine that would cause this. The valves on the engine may also be chattering.