@Veqryn:
question 1) can you take an empty territory with a single tank, then move 10 mech infantry through it to attack the enemy territory beyond it all during the combat phase?
No.
@Veqryn:
question 2) can you take an empty territory with say, 3 tanks and 3 mech infantry, move through it and attack the enemy territory beyond it, win that battle, then during the non-combat move, back up that territory by moving 10 mech infantry there through the now conquered enemy territories?
Yes.