as long as lockjaw is just carrying someone and not using the hit and run, can he use his phasing?

also, can ghost rider carry someone during his running shot and not suffer a -2 to attack?

i say yes to both of these, but we have been running into some problems.

Also does a transporter Take a click if they use DT? I heard he doesn't.

Yes. Transporters function exactly like fliers, as far as carry characters. You do not need to perfrom the move and attack just to carry someone. From the Icons rule book (page 18, under 'Carrying other characters'):

Carrying other characters. During movement, flying characters, characters with the transporter ability (transporters), and characters using certain
Feat cards, powers, or team abilities can carry other friendly characters that have the dolphin or boot speed mode. Flying characters, double base characters, transporters, giant characters, and big characters cannot be carried. A character can carry only one character per turn. A character that can carry other friendly characters cannot pick up or carry a character that is holding an object but, if its abilities allow, the character that can carry other friendly characters may carry both a character and an object.

See all that is required is that the transporter is moving; not that you actually give it a move action.

What do you think?

From the Double-Time description:

When the character is not adjacent to an opposing character and is given a move action, it may move up to double its unmodified speed value; it may not make attacks during this move action. At the end of the move, if the character is not a transporter, deal it 1 pushing damage that ignores Willpower and team abilities.