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Vacuum leak possible, smoke the intake, ignition timing, compression test.
First is it hydraulic or air suspension, if air, there could be a few options, vent valve, air line issue, broken or cracked air bags, etc. Hydraulic, leak, oil reservoir low, etc.
Yes they are the same, under the center console at the transmission shifter.
Check the seal of the hose that goes between the radiator and the reservoir, make sure the cap is not faulty, might need a better quality radiator cap.
Does it have a rubber 'O' ring, lube the o-ring before installing it.
Sounds like a good thing, but the question I have is why did the engine have to be replaced. You show a 2011 on your post, so I assume you have a newer one already. If so you are already familiar with them. Make sure it is a good prices, and don't let them get to you just because they state new engine, get the paper work and research.
I have repaired many different oil leaks, but without looking to find out where the leaks is, I can't tell you what to fix. Have someone look at it and find what is leaking. Possible, oil pan, front or rear seal, valve cover gaskets.
Is there any codes ?
The computer is the voltage regulator, does the light go off when it reaches 14.5 volts. Have it tested, it sounds like the computer has an issue, but the alternator could have a diode issue as well. The computer can be by-passed with a good mechanic.
In a lot of cases it not the EGR but the fuel. Pressure test your fuel, and check your fuel filter.