The user groups available for checking when the discussion board is created determine the board access if board membership is enabled, i.e. which user groups will be able to see the board.
When it comes to editing/deleting content on the board, that is reserved for administrators and moderators of the board (notice this is on discussion board level, not per-topic level).
Users are only allowed to edit/delete their own posts, but not the whole topic (again, this is for moderators and admins only).
What you asked for is that each user becomes a moderator/admin for his own topic and that functionality is not present out of the box and requires additional coding to be achieved.
You can do it yourself and ask for some additional pointers on how to do it, or you can issue a new feature request for future versions of MonoX in the roadmap discussion board.