Yes, shortening the rope is a very good idea.
I usually aim for about 20m.
Yes, you have to be in tune with your partner and move at roughly the same pace.
Simulclimbing IS "free-climbing" (as opposed to "aid climbing").
"You must not fall" is the mental mantra to keep you focused on each foothold and handhold and to keep three points of contact at all times. Of course, if you were absolutely sure that you weren't going to fall, you wouldn't need the rope, but even when we think we are absolutely sure about something, we can be wrong.