On some missions, your Imperial Figures get to do actions at the end of the Rebels activation. Do these actions count as activations, i.e. would you get the movement points from Ringleader and/or Prepare the Ambush?

Do you mean when instead of activating normally, a specific imperial figure activates after each rebel activation and has only one action?

Yes, they are activations that have only one action, so Jyn can Quick Draw, and Infrared Scanners, Prepare the Ambush (if the first activation of a round), and Ringleader would apply.