One guy at the venue I play at quite often runs cloak and dagger Duo. It has raised a few questions. So if anyone can help clarify it would be appreciated.

First off CandD have the transporter symbol, the duo attack symbol and phase and teleport.

If they use Phase/Teleport would they be able to make a transporter move and shoot? I figured they wouldn't be able to because Phase/Teleport requires a power action.

My second question is if CandD use the transporter move and shoot ability can they also use the Duo attack ability? I also thought this was a no because the Transporter requires a move action and the Duo attack requires a power action.

And one more question that arose which kind of involved Cloak and Dagger. I was running Nightwing with Vendetta to Cloak and Dagger. Iron Fist did most of the damage to Cloak and Dagger but Nightwing hit them last for 2 which put CandD on their last click. My opponent attacked the next turn and critically missed, should I have received the extra points for Vendetta since Nightwing was the last one to damage Cloak and Dagger?

You would be correct.

You can only give one non-free action. The PT requires a power action. The M&A requires a move action

Correct answer...incorrect reason.
M&A is a move action which grants a close or ranged combat attack. It does not grant a power action.

No. Though he was last to hit them, he did not KO them.