Thanks for these questions. You're right that the rules aren't clear, so I've updated the PDF to 1.2.
To answer your questions:
- The omega-drive adds one extra move and attack, for two of each, total.
- It's assumed that the mech docks between sectors, but you don't need to do it manually. Because of this you choose a launch zone at the start of each sector.
- Once you've defeated the last enemy in the sector, you can move on to the next immediately: no new enemy, and no event.