2) Yes, you can run into a star on purpose. Personally, I think only single one man craft should be able to do it (after all, if you were a wingman or crew member, would you LET your leader ram you into a star?), but presently any and all ships can.
If you abort, and exit hyperspace in a system that happens to have a sun on the edge, you can hit it and be killed. Exactly what happens depends on the size of the ship. Fighters and I think freighters are destroyed Capital ships just take damage. It's in the Rules somewhere the exact results.
"May the Grace of Ara go with you, and His Vengeance be wrought upon your enemies."
There are no stars in hyperspace exit points, if you abort you may end up in one though as you don't come out at an exit point. When flying into a sun freighters and fighters get destroyed, capital ships take damage+the pilot die+everyone else on board gets knocked out.
Yes, systems shouldn't have suns on the edges at all. If you happen to encounter one let Kyle know; I believe he's the one who has been working on fixing that.
There was also a bug for a time that resulted in players dropping out of hyper normally in the middle of systems, and a few ended up in suns as a result, but as with all bugs, the effects are of course reversed.