I know that when you have a character that is carried by a flyer, you cannot give that character an action. What about if you have a transporter that transports a character? Can the character take an action? What about a non-flyer transporter?

NAAT or No Action After Taxi applys to ALL the above examples.

Carry(Flyer or Transporter)=no action
TK=action

To put it in a way that doesn't use acronyms: No figure may take a non-free action if they been carried by any means.

When in doubt, feel free to ask multiple questions (about any mechanic) in one thread. I'm not trying to be a jerk, it's just that instead of creating a thread for each question and bouncing between them all, you could get them all answered in one place...usually by the same person.