hockeyplaya13- You really oughta get "Super Squats" and learn how to do this stuff right
If you do the squat sets with proper intensity, you won't be able to follow with immediate calf work, or do any worthwhile work on the leg press; you'll be lucky if you can walk across the room normally

I know that *I* sure couldn't do anything at the end of a good set of squats except breathe and try to write down the set info in my training log, and even doing *that* is often a serious challenge. Instead of leg press work (yeah, I know it's satisfying to do big numbers on a leg press

) you'd be better off doing another set of squats if you have the oomph left in you. But tough sets of squats are incredibly hard work; about the hardest thing you can do IMO.
I go for lower reps with hamstring work, very seldom over 15 reps/set. Some people say to do even fewer. The 20 reps on the squats are a weird, separate issue; most sets of any exercise should last between 20-70 seconds (with those numbers being the extreme ends of the spectrum) and 20 reps done at the right pace/tempo take a very long time.
This is where you need to study up on fast and slow-twitch muscle fibers so you understand how long to work a muscle (I like The Poliquin Principles, another good book). Getting the most out of exercise takes more study/understanding than most people might think.
I don't really understand the "as I do my last rep in each set of squats, I bring my legs in a little and do as many calves as I can" part of your post. To do calves you gotta step up onto a calf-block and you'll use a *lot* more weight than you do for your squats...so it's not like something you can throw in at the end of a squat set
Do the squats, then the stiff/semi deads for hams, then calves. I do one set for abs and then some gripper work on leg days, though my grip work is sometimes compromised by having held the bar during the deadlifts (do *NOT* use straps, hold the bar with just your hand strength).