Update (if anyone's paying attention... lol)... I'm 99% sure it's a grounding issue. I believe one of the 3 wires is a "ground" wire... I'm going to take out the radio again and check to make sure it's getting a good connection and is in fact in the correct terminal.

As for the other issue, it seems to be fixed after I further tightened the screw that holds in the main radio... Still need to see if it happens again over time.

If none of the above work -- and no one hear has any solutions -- I guess I'll bight the bullet and take it to the Dealership.