strike 3 hits batter

[paulis]

I am not an umpire but have a question. My understanding is that if a pitch hits a batter, the ball is dead and no runners can advance beyond one base if forced to do so. My understanding is also that if a batter swings at a pitch and the pitch hits the batter, it is a strike. In this case, is the ball also dead or if strike three is swung at and the ball hits the batter and bounces away, runners can advance at their own risk? If so, does that mean than a winning run could score on swinging strike three that hits the batter and bounces to the backstop? What is the rule here?

Thanks