For your first question, (OBR 6.06c notes) if the batter is in the box, the ball is dead once the batter's backswing hits the catcher, with one exception. The runner returns to first and the count is now 0-1. The one exception is if the catcher is able to throw out the runner, then the out stands. Now, if you judge the batter hit the catcher on purpose then the batter is out and the runner returns to first.
Your second question I'm not a hundred percent sure, but it would seem to be batter interference, and therefore the BR would be out.
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