If a B-Wing with Advanced Sensors starts its movement phase on a rock, but would not have its movement template overlap any of the rock on that turn (i.e. it would be free to take an action after moving so long as no stress is on it and it doesn't bump anything), can it use Advanced Sensors to take an action prior to moving? Does it depend (for example, I would assume you can't barrel roll if the movement template for the roll goes over the rock)? Sorry if this has been answered elsewhere and I missed it.

Thanks!

As long as the template for barrel roll doesn't touch the rock, you're fine.

Note that you are not prohibited from taking actions becouse you are on an asteroid. Landing on (or passing through) one removes your take action step that turn. You are still free to take any actions comeing from other sources.

Here's my understanding, based on your scenario:

Case 1 - Performing the Barrel Roll action:

Does the Barrel Roll template overlap any part of the asteroid you're sitting on?

Yes - Cannot perform the Barrel Roll

No - Perform the Barrel Roll, provided the template doesn't overlap any other ships/asteroids

Case 2 - Performing any other Free Action via Advanced Sensors while overlapping an asteroid:

You can perform any legal Free Action listed in your ship's action bar.

Really, I tried to condense what you can find here: https://teamcovenant.com/buhallin/2013/04/12/all-about-obstacles/ Don't take this as the authority, but it makes sense.