2008 cobalt

Yes! My car has done similar things. First have the battery load tested. If it fails, or if its more than five years old replace it. That may solve all your problems like it did mine a few years back. Also have it scanned for trouble codes. The computer may have some stored information telling you where else to look. Also electrical connections on older cars can corrode or start to allow tiny amounts of moisture in which can cause all sorts of weirdness. That's probably a job for a shop. Hope some of this helps.

Mine did this and so would shut off on it's own from time to time. I put a better ground from the computer to a bolt on the car and it fixed everything. They don't do a good job grounding these and they interfere with themselves.