Yes, it could.
Sounds like P.S. belt may be slipping either adjust or replace
Could be low on coolant, a stuck open thermostat or a partially blocked heater core.
i would make sure that the engine is idling at the right rpm cause to fast of rpm can cause that for sure
I would suspect a weak EGR valve. It should be toward the rear of the motor. Take a non or low flammable spray (WD40) and spray on or around the valve and on and around the seals and if the engine smoothes out that is where the problem is. A severe vaccum leak causes a lean condition which in turn causes the problem you have. Also spray around the hoses, gaskets, etc.
It can.
No, but something that could cause uneven idle could cause the check engine light to turn on.No, but something that could cause uneven idle could cause the check engine light to turn on.
When an idle control value is clogged the idling speed of your vehicle will change. The car may also stall when you turn on the air conditioning.
you may have a bent valve
It is supposed to keep idling when you put it in park, unless you turn the ignition key off.
There are several things that could cause this. The first thing to investigate, though, is the idle speed your engine is set at. As with any engine, if the idle is set too low, the engine will not continue running.
The engine is running rich. Clean or replace the spark plug and the air filter. If problem persists, close (turn clockwise) the needle valve on the carburetor 1/8 turn.
No the EGR valve has nothing whatsoever to do with the brakes. It is an emissions control device. -But since it could affect a little the idling rate of the engine, and since the engine when idling generates more vacuum that by its turn assists the vehicle brakes force needed to act on the pedal, indeed it could "affect the brakes" a little. Not directly; as I described the driver would need to press harder on the pedal to get same breaking results as he/she is used to, maybe leading to some sort of dangerous situation.