High noise = Interference.
I started untangling and unplugging cables. I untangled the monitor cable and had it run away from everything else. The noise decreased to -77 dBM. This is still high but it was enough to improve the Wifi speed to 15 Mbps.
Then, I unplugged all of the cables from the Mac Mini and turned off the monitor. Then, I used Remote Desktop to connect to the Mac Mini. The noise went down to -93 dBM (identical to the laptop noise). The Wifi speed was 15 Mbps but Remote Desktop was using some of the bandwidth. Therefore, it was probably really 20 Mbps.
Now, when I plug the monitor into the laptop computer, the Wifi signal for the laptop goes down to -77 dBM
So, the interference is from the wires. Problem was reproduced on laptop (MacBook Pro 15), so I can't really blame the Mac Mini as the problem.
I hope that my explanation of my testing is clear enough to show others how to troubleshoot if they have similar problems.
So, I guess that I need to try using a Wifi booster to get a better signal to over power the noise and/or upgrade my WiFi to 801.11ac.
Also, I need better shielded cables. When purchasing cables, how do you know which have better shielding?