VVT code and rough running engine

Bought this car knowing it has few issues. But drives great and engine is smooth when I started it and drove it to the gas station and back, soon as I entered my driveway and parked the RPM started jumping up and down, then smoothes out, then does it again. Read the code and found these, while I was trying to read more stuff the engine starting to sound weird, similar to what it would sound if one has bad gas, then smoothes out, then does it again. Then 2 minutes later I saw smoke, so I turned it off. When I bought it the coolant reservoir was low so I added some but can't see any water leaks. I'd there something underneath the top plenum that is common to leak? Not sure if the smoke is coolant related or related to the VVT code, or just 2 different issues. I attached pictures and videos. One of the pictures show the options I have for active testing that I could do, I did a couple but not sure what I should be seeing in numbers. When I first got it it had several codes unrelated to each other so I deleted all, changed the fob battery and waited and some codes to come back and only the p0174 and p0171 came back which I asked on another question. But now these are the ones am seeing and the check engine light is not on.