Not real clear about this. If a thrown ball to home plate hits BR's bat (which is positioned somewhere around home plate), is that a blocked ball or a live ball? I am pretty sure that is a live ball, but want to make sure.

Yep, it's a live ball, keep on a goin'. If the ball had hit a bat laying in foul territory and it was any other bat other than the batter's it's a blocked ball. The batter's bat is considered part of the playing field and no penalty for the ball hitting it, unless the batter throws it at the ball.

agree