either a blown head gasket or a cracked head head gasket
Coolant leak.
Probably a coolant leak.
You have a blown head gasket
Loose exhaust system.
that would be a head gasket
Elictrical fire or burnt out relay. Look for physical signs of fire, burnt wires. Where there's smoke there's fire
under the drivers door under the drivers door
Not likely. Smoke from under the hood denotes a leak. Either your coolant or oil is leaking. White, thick smoke is oil. Could just be a gasket. Thinner hazy smoke is coolant. Check your hoses. Look for fluids/wet spots. Bad plugs can missfire, and make your exhaust smoke.
The only way a bumper can create smoke is is it is trailing on the ground. There are no 'mechanical' parts in a bumper. The end of the tailpipe is probably located right under the bumper and what you are seeing is smoke from the exhaust system. You should have the vehicle checked out as smoke from the exhaust is usually not a good thing.
bad heater core under dash
Yes It should all burn off eventualy.