2008 Aveo LS issues in cold weather

I experienced similar things to a much lesser degree this year but my car seems to be going down a pretty swift spiral at the moment.

Here are the basic symptoms:

Car would die but electric components would stay on (power steering out, no acceleration, etc./radio and lights remain on.) When this happened the check engine light, battery light, and sometimes the oil light came on. (Got a new battery and a fuel line cleaning last year.) Sometimes this happened right after starting my car while I was letting it warm up and was outside scraping. Typically while driving, it only died in this manner during breaking, idling, or driving very slowly.

While driving, the car would stall- suddenly acceleration would stop even with the foot on the gas, then would get a burst of acceleration and she would keep going like nothing was wrong. The check engine light would pop on during this but turn right back off.

Low RPM idling- typically my car during normal weather idles at about 1k RPM after a cold start, it now idles at 500 - 750 RPM.

Rough turnover when starting the car- it sounded like she was struggling to turn over, and when she did it sounded different than usual (loud, revving, higher pitched.)

My NEW issues are that my check engine/emission light is constantly on. I thought it may be due to the extreme cold that we've been having, and was intending on waiting for it to warm up a bit over the weekend and into next week and if it didn't go away get it checked out. However, that idea was nixed when my hold light began flashing and not shutting off. My car is now running roughly, seems to not like going over 30mph or even the journey to get up to 30mph, and it feels like overall the car is just struggling to run.

Typically these issues go away after the car has warmed up for awhile. However, they're taking longer and longer to go away- I'm thinking it's a combination of a failure of something and the extreme cold we've been having lately here.

It's in the shop now- they're unable to duplicate my issues (which is typical- these are common early in the day when leaving for work and it's been very cold over night, but not as common at the end of the day when leaving work.) They've pulled 3 codes, and the phrasing he used was "PCM issue", "ECM" issue, "communication code", and "engine coolant temperature sensor error".

Has anyone run into issues like this or something similar?