When my troops are moving into a territory an enemy is evacuating, does this start a combat? Or do all move orders happen at the same speed, so that he has already vacated by the time my guys get there?
All movement orders in friendly territory happen first. All other movement orders happen after that. That means that the enemy has already left when your troops get there.
All magic happens before movement, so teleportation etc can be used to catch enemy armies.
Hiding/sneaking happens before movement, so you can't fight a stealthy army unless it attacks.
I'm not quite sure about this, but I think that moving army away from a besieged province (which still owned by the defender) happens after the defender has moved his forces there, so there'd be a fight.
What happens when units from province A, owned by nation Y, invade province B, owned by nation Z and in the same turn the troops from B invade A. Do they switch over, or does combat occur?