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Body weight squat, goblet squat, zombie squat, front squat, and back squat
mainly your legs but and your back a little
the difference in the amount of force is getting over complicated, the front squat is just another variation of the squat. Do the one that you are most comfortable with. Always use a spotter or a safety cage when doing sqauts. Go as heavy as possible squats and deadlifts are the hardest exercises but you will see massive increases in all your body if you do them regularly
Yes, it is a secondary muscle (synergist/stabilizer) used in the squat. There is a link below in which you can get a chart of the muscles used in a squat: go down about halfway and you'll see the chart.
A good squat exercise is the front squat in which the bar is placed on the front of your shoulders rather the back (very painful but rewarding). The wide grip bench press strengthens your upper body well.
Box Squat is a variation of a squat where you sit on a box and squat back up.
i dont know all of them, but your calves will be limp noodles the day after you do a bunch. thighs and butt, probably, too.
The squat works many muscles in the body in some form. The primary movers are the hamstrings, quads, and glutes. Assuming you are doing them correctly with your knees out and squatting below parallel, you should be using your hip adductors as well.