Re: 20 rep squats
A few years ago I did 5 weeks worth of a 20 rep squat program after I'd hurt my shoulder and couldn't do upper body stuff for awhile. I subtracted 80lbs off my 5RM and started there, squatting twice per week and adding 5lbs per squat day. Towards the end I was often resting 6-8 seconds between reps, and I would usually add in some RDLs and a quick conditioning workout then call it a day. If you keep that up for 8 weeks and eat/sleep enough, you'll be squatting your old 5RM for 20 reps.
Those 5 weeks led me right up to a PL meet which meant I had to recondition my CNS for maximal efforts rather than 20RM efforts, but after two weeks of getting used to weights in the 1-3RM range I found that my 1RM had increased by about 35lbs....not a bad gain for less than two months.