I've looked for this for a while, and can't find anything.

I have a (small-based) ship that took a barrel roll action in the activation phase. In the combat phase, my opponent shoots said ship with a tractor beam, giving it its first token. Can he choose to barrel roll my ship that has already barrel rolled this turn? Or can he only boost it?

If I had multiple actions with the same ship and both boosted and barrel rolled, and was then hit by a tractor beam, can my opponent do any movement of my ship?

Yes, he can make you boost or barrel roll even if you already have done a Boost and/or Barrel Roll action previously.

The reason is that the Tractor Beam is simply making you "perform" a boost or barrel roll; you're not actually carrying out the corresponding action. Same principle as a ship performing a Focus action and then later being assigned a Focus token.

You can only perform a particular action once per round, but if the effect in question doesn't have the word "action" attached to it, then you're not performing that action. DR4CO's examples above illustrate that.

Take this for example, a TIE Phantom decides to decloak using a barrel roll, and then when it comes to his Activation phase, he makes a manoeuvre and then performs a barrel roll action. In the Combat phase, he is hit by a tractor beam and the opponent decides to barrel roll him again. That's three barrel rolls during the round, but only one of them was performed as a barrel roll action.

Aha, didn't think about how decloak was worded. Should have looked at that, given how much I've played Phantoms.

Also, the reference card says it's not an action or a maneuver.

Taken from the FAQ, page 2: