You cannot push people off boards; the edge of a board is a barrier. If pushed into a pit, they would respawn at the nearest, legal respawn point.
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When respawning, if someone is already on the respawn point, do you treat it as if landing on their head if you choose to re+spawn there also?
You spawn on a safe space adjacent to the spawn point.
Does your movement end when you respawn?
Yes, unless you are forced to respawn before starting your movement phase.
When respawning, do you get to choose your orientation?
Your Q is up and you can face in any direction you like. Your movement ends.