I've never used them but plan to tonight. When forcing your opponent to barrel roll or boost onto an obstacle is it ok that the template also overlaps the obstacle?

Yes.

Definitely check the Tractor Bean reference card (and have it handy if possible).

56 minutes ago, ObiWonka said:

Definitely check the Tractor Bean reference card (and have it handy if possible).

I'm sure you meant to show that as a Tractor Bean:

3 hours ago, ObiWonka said:

Definitely check the Tractor Bean reference card (and have it handy if possible).

Definitely check out the errata for this card, there's some small but important changes.

In fact, as I think more about this, you can make them roll for damage and lose their action even if you cannot land them on an obstacle by virtue of the template overlapping an obstacle.

I got FAQed.....

They won't lose their action unless they go over it with a manoeuvre, per the latest FAQ.

I have a follow up question: if you tractor beam a (small) ship, do you have to move it or can you leave it in place?

You can leave it be. Check out the errata text I posted above, it added the word "may" in there.