To answer the "why run" question: you're right, part of it is that the person you need to rescue is being carried off and you need to chase down their captors. Another part is that you'll see where the enemy is planning to attack on their next turn, like in the game "Into the Breach", so you may need more movement in the actions you have to get out of the way.
As for knowing which direction to go, I haven't decided that yet. It's an important consideration when you can only see three steps away from yourself. Perhaps, your magic armour has some kind of homing beacon that points to your charge. I still need to figure that one out.
Thanks for the questions!