Really weird ignition sequence and rough idle
 

I have a 2004 Cavalier LS Sport automatic sedan that when first cranked has a weird surging idle sequence that where it surges and then dies back, and flips between these two for about 30 seconds and then idles properly. The car runs great otherwise. To see what I am saying I recorded a video and uploaded it to YouTube, you can see it here: I have swapped many parts including the idle air control valve, the ignition coils, the ignition control module, the throttle position sensor, I have cleaned the throttle body, I have tested the fuel pump and the pressure reads a constant 55 psi, and I have used injector cleaner. Does anyone know what this may be?

More information and update.
 

Hey all, I'm taking another attempt at this so I am back with more information on my issue now that I have had a chance to drive the car a little. I am fairly certain there is some form of water/coolant leak, as I have to add coolant every 150-200 miles or so at approximately 1 pint or a full bottle of water every 150-200 miles, and if I crank it after it has sat undriven for a few days it will blow thick wight smoke for about 5 minutes and a large outline/parameter of condensed water/exhaust will accumulate on the ground behind the tail pipe. From Googling the symptoms I have seen indications that this could be a leaking head gasket but I wanted to run this by you experts before I undertook that endeavor, to see if maybe there were some other common (or more likely) causes for this that I should try before replacing the head gasket. I bought it from a car shop that had just replaced the motor. They put a 2.2 Ecotec in that came from a 68K mile cavalier into this one that had over 220K on it at the time, so are there any common mistakes/issues that arise after a motor swap that lends itself towards a water leak and water in the exhaust. I am ignorant on this type of issue, as I have never done coolant or exhaust work before.

I will add that there is something wrong with the gauge cluster or something wrong with the fuel system because the gas never shows full, even though when I fill up with gas the tank overflows because the nozzle never shuts off on this car, and the fuel level indicator is slow to show an increase in level after filling up like it is unresponsive. I have tried swapping out the fuel cap and replacing the vapor purge cylinder but no change, and again about 55psi when testing the fuel pressure. I have read that there is a common issue with the motor on the fuel level indicator on the gauge cluster, but I was wanting to run this by you guys to see if it might be related to the coolant leak before I started throwing money at parts, or even worse, try taking it to an auto shop in Atlanta to see how much it costs to diagnose. When the car is first cranked it will rev and die back in a jerking manner and this can be seen in the surging rpm indicator in the video I posted before, I figure this is related to the coolant leak but I wanted to mention it because it is another thing I noticed. Also, at random points while driving I can smell a slight gas odor in the cabin and I do not know what might be causing that. I have inspected the injectors and cannot find any indication of leaks and they sound healthy when in use. Is this another issue or is it related to the fuel level issue maybe, any suggestions would be much appreciated? I had a great 2003 Cavalier that I drove without issue for 5 years and fell in love with the car, so I do not want to give up on this one right after having bought it and would really like to learn how to take care of these cars.