OK, so Apple cannot get me a replacement unit; they want me to send this one back, wait 1-2 weeks until they've verified its arrival, and then they'd order the replacement - which has to come from China. Looks like it will be at least 4-6 weeks.
So, I've decided to wait a little, and see what I can figure out.
Interestingly, because I erased the Mac Mini at Apple's recommendation, I had to reinstall Big Sur. It downloaded and installed Big Sur 11.1, which would be what I expected. I DO NOT SEE ANY PINK PIXELATION, and its been almost 3 hours.
I also have the issue with Bluetooth, so I decided to do a little experiment. I figured it was either a bad chip (which doesn't make any sense, or Broadcom wouldn't keep selling them, right
, or its a bad antenna with the keyboard and mouse always loosing the signal and connecting/reconnecting. So, I turned the Mac Mini upside down - it is now sitting on its top, with the round black plastic piece pointing up. And guess what - I've had no drop outs from the mouse or keyboard for about 2 hours and 45 minutes.
So, either being upside down helps the pink pixels (I don't see why unless the HDMI cable fits better upside down), or it was the CLEAN install of Big Sur 11. 1 which helped the graphical issue.
As to the Bluetooth, being upside down does make sense, as the plastic bottom probably allows more signal to escape, and the bluetooth signal to the keyboard and mouse are stronger.
I'm going to run it this way for about 6 hours (about 5 PM CST), then I'll flip it back on its bottom and see if the keyboard and mouse issue reoccurs. Hopefully this will narrow down what is going on.