can transporters use the duo attack while making a transporter attack?

no. Both are abilities that require a power action.

Nope. The Move and Attack ability grants you a close (or ranged) combat attack, while you must give a power action to activate the Duo attack ability.

EDIT : @ChiRocker : the Move and Attack ability recquires a move action, not a power one.

GTK, that's what I get for not checking why.