Yes, probably a ground connection.
I agree that the problem is starting to sound like corrosion and grounding concerns. I note that you changed the brake light switch but was unclear re the tail light bulbs, in particular the signal and brake light bulbs.
The business of the one rear signal light fixing itself is probably ground and corrosion related, however a filament could be near broken. If so, it may be generating out of norms resistance signals that are being picked up by the monitoring circuits and hence triggering faults.
I would certainly be replacing that one bulb and perhaps all the rear bulbs, but with genuine LR sourced bulbs rather than chain store bulbs due to quality control issues. I figure the LR bulbs go thru some sort of quality control test and the chain stores get the rejects.
I find a low battery/hard start situation can sometimes cause the radio display to disappear or display oddly. Usually for me, the display returns after a few normal engine restarts however on occasion, I have had to do the hard reset thing. Most recently, I recall having to do the hard reset just after the alternator was replaced but do not know why, just needed it.
The business of the rear fogs going on suggests corrosion. I have a theory that with each the rear light assembly grounds being sort of common, that if the ground was faulty, that power would flow "backwards" into many of the filaments. The backup lights are a case in particular and perhaps also the rear fogs as well, but I have never thought much about them.
Overall, it sounds like you are resolving the problems. I think that as is often the norm, there is more than one problem and hence that is what makes resolution so difficult.