1. When you MC a mob there are two ranges. The range the mob moves from you, and the range in which the mob moves from where it was initially MCed. I've tested this extensively. If the mob moves out of either, you lose control of it. The range is 30 yards from either target (you or the MCed unit).
For example: If you mind control a unit that is 20 yards from you and run it toward your player, and past it another 15 yards in the same direction, you will lose the MC.
If you mind control the same unit and run it 15 yards in the opposite direction, when you are 20 yards away, you will lose the MC. The ranges seem very strict.