1. Can a transporter like Nightshade use Phasing and carry another figure at the same time?

2. Can Nightshade Phase and use Move & Attack at the same time?

3. Can Nightshade Phase, Move & Attack, and carry another figure at the same time?

4. Can Lightspeed carry another figure away without rolling breakaway? (the figure being carried is based)

5. If Flight is outwitted, can a flyer still carry another figure?

Yes; the Carry ability lets you carry whenever you move as a result of being given an action.

No. Phasing requires a power action to be given, while Move and Attack requires a separate move action to be given. They can't be used as part of the same action.

Yes. Note that she can also do this without using Phasing as long as she herself is not starting adjacent to an opposing character.

Yes. Flight and Carry are two different abilities, and Carry would need to be outwitted instead of Flight to stop you from carrying.

Rep to flatmatt for beating me to the answers. He is correct

Thanks for the answers. I like your mods, especially Lockheed.