Is there a rule in the MLB involving collisions at home plate?

Answer 1

Surprisingly, no.

Rule 7.06 states that a catcher may not block the plate unless in possession of the ball. Other than that, once the catcher has or is about to get the thrown ball, it's a free-for-all. The catcher can block as much of plate as he wants with any part of his body, and the runner can do just about anything to knock the ball out of the catcher's mitt. Although this has resulted, on several occasions, to injuries (sometimes serious) to the catcher (and sometimes the runner), Baseball rule makers have never made any attempt to define what is and isn't permissible in this circumstance. Horrific collisions at the plate are just considered part of the game.

Note, for instance, in the video below that the runner VERY intentionally rams his elbow into the catcher's neck, and neither the umpire, manager, or even the catcher think anything of it.