I know to a certainty that at least one heavy Batman team is showing up at my venue tonight, so I figured I'd ask these now. My presumed answers follow each question but I'd like some feedback. Thanks in advance!

1) Do vehicles count as characters for the purposes of interacting with theme team rules? (My read: yes, because why else would they have keywords?)

2) Are vehicles valid targets for the use of the Support power? (My read: yes, though it makes more sense mechanically than thematically)
2a) If so, can the pilot of a vehicle use Support on the vehicle they're piloting? (My read: no, because they aren't technically on the map while they're piloting the vehicle, unless the vehicle's rules specifically allow the use of the pilots' powers)

3) Can Oracle use the Batwing, Batmobile, or Batcycle as characters through whom to trace line of site for use of her trait? (My read: yes, due to the answer to 1 above)

Please tell me if I got these wrong - thanks!

1) Yes, they are characters.

2) Yes, they can be healed. No, the pilot can not use any tame effects unless it specifically states they can while they are the pilot.

3) Don't know the power, you should quote!

"If Oracle is not adjacent to an opposing character and is either in her starting area or on elevated terrain, she can draw lines of fire and count range and squares from the square of any single friendly character that has the Batman Family, Birds of Prey or Justice League keyword. "

But given the answer to #1, the answer is "yes" as I'd suspected.

Thanks!

Vehicles
A vehicle is a HeroClix character marked with the :d-steering wheel: defense symbol.

That should answer all of your questions.

EDIT: except 2a. Which is answered by:

A character who becomes a vehicle's pilot is removed from the battlefield and placed on the vehicle's character card; all of a pilot's powers and abilities are ignored, unless a game effect specifies it activates when the character is a pilot.

i fixed your wheel for you.