Sorry for the belated answer!
The game is designed to work without having to erase anything, so yes, power you assign this turn will stay on for all future turns, until the cells are damaged.
Linking works exactly as you described: shield activates because of enemy attack, and in turn activates your weapon, enabling a counterattack.
Yes, Missiles are spent regardless of the outcome.
Yup, your powered cells get damaged first, making the hardware have less power available.
Thanks for catching the scout-pathfinder typo! I'll upload a fix shortly.