My 2004 impala idles shakes like as if it wants to shut off and I smell coolant when the car is parked it also looks like it wants to over heat

SOURCE: My 2001 ford windstar lx van smells like coolant when i drive

Several things to check. Have the cooling system pressure checked. A quick and simple test. Puts system under pressure and helps to locate a leak. The coolant doesn't just go away, it's got to be leaking either externally or internally. Be sure that the radiator cap is checked too. It needs to maintain the proper pressure for the system
Sound like coolant is leaking on the exhaust system. This can result in the smell and you will not see a leak as it is evaporating when it hits the hot pipes.
Good Luck

SOURCE: After start, eng. shakes at idle. 2001 VW Jetta

if it has a 1.8 coils are bad but check mass air meter and throttle as well

SOURCE: 2004 Chevy Impala no heat from defrost or heater

No heat is often a symptom of low coolant, usually followed by overheat. There are other controls that regulate heater, but right now, re-fill the cooling system with engine running and heater on high, then check for leaks (coolant you lost went somewhere...you need to determine where) Low coolant will damage your engine. Take care of that first, then if heater still does not work, then do diagnosis on that. (if you loose the engine heat won't matter, will it!)

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SOURCE: 2003 chevy impala impala shakes when brakes applied

If it only happens when braking, then it is definately you brake system. Most likely you rotors and pads need replacement. If you can do car work, then this is not a difficult job, but requires some wrenches. The parts can be purchased a lot cheaper on-line. A shop will get you for $300-$800. I bought all my parts for my 2001 VW passat for $200 shipped to my door. Good Luck.

SOURCE: Cold start-extremely rough idle-Shakes,smell fuel

Black smoke means buring rich. Have the vehicle's ECU scanned for codes and do the repair the codes describe. I'm gonna take a stab in the dark and say Mass Air Flow Sensor.(MAF)