Re: 20 rep squats
Randall Strossen brought 20 rep squats back to the training world in the 90's with his book Super Squats. Basically the program was either 2-3 days of full body workouts. Squats done for one set of 20. Using your 10RM to get to 20 reps done as you described--almost rest pause fashion with the bar on your back. Then it was 3-4 more exercises for either sets of 5 or 10.
Dr. Ken Leistner is also a big fain of 20 rep squats. I think at around age 50 or so he did 405 for 20 reps at around 165, maybe lighter. He's a big fan of training to failure. He recommends training twice a week something like (warm ups not included):
Stifflegged Deadlift 1x15
Bench press 1x6, 1x8
Weighted Chins 1x6, 1x8
Shrug 1x12, 1x10
Press 1x6, 1x8
Barbell Row 1x6, 1x8
Barbell Curl or Farmer's Walk
As mentioned earlier, Stuart McRobert is another fan. Note that most 20 rep programs that make you take it to the limit are abbreivated due to the demands.
20 Rep Squats will teach you intensity and knock you out. Make sure to eat and sleep. They will make you stronger especially in reps, but most have not gotten a big boost in their 1RMs.