Weird warning indicators and check engine light?

Hey guys, I had a few questions, I live in central Illinois, and we're starting to get into our snowy season, which, usually when that happens, I get the typical TPMS warning, however, this seasons been sort of weird.

So, it started with the TPMS warning when we got our first snow, I checked the pressure all around when I got it to my garage, and they weren't too low, so I figured I'd let it be until some of the snow got cleared, however a couple days later, the TPMS warning went off, does that usually happen, or could the pressure have evened out deactivating the TPMS warning?

Then, a couple of days ago, I filled up with gas, and yesterday I got in, started it up and had a warning indicator, and a message stating that I needed to tighten my fuel cap, I've had this one before, and I had tried to tighten it, but it eventually just went away, so I figured this was the same thing, however tonight when I got in and started it up, my Check Engine light came on and the car said I needed to tighten my Fuel Cap or there may be an issue with my Emissions System...not too sure what to think about this one? I need an oil change anyways so should I just have the dealership look into it? Or have you guys seen this before?

Kinda nervous about it...as I don't want my baby to start having issues :whyme: haha, let me know what you guys think!