Its a new feature in Rebellion. Each star has the standard antimatter restore ability plus an additional one. I don't remember which one has which, but there is +20% shield regeneration, -10% shield mitigation, -50% shield and hull regeneration, and +15% weapon cooldown but -10% weapon range.

Nope

I think you think its a bigger deal than it is. It only applies in the Star's gravity well, not the entire solar system orbiting the star. Unless you're playing multistar maps or the star happens to be a main chokepoint its pretty trivial.

Just click the star after you scout it to see the abilities.