[Taera]

When you are out of supplies:
1. Yours shields wont work
2. You move 1 move per turn
3. Your weapons work 50/50 (if you have two rockets, one wont fire)
4. You cannot use any special ability = mining, cloaking etc.

For the supplies question, everything that uses supplies use them only when actually used.
This means that every damn missile you fire in the combat drains some of your supplies. Every. I mean it.