I would like to know what the difference between my leave and my leaving is.
e.g. Are you all right with my leaving/leave?
If you mean “act of leaving” (i.e. departing from some place) then it should be “leaving”. As a noun, “leave” means permission to do something, especially permission to take time off work, or a period of time taken off work. (An exception is the set expression “take one’s leave”, where “leave” does mean “act of leaving”.)
“Are you all right with my leaving?” – Is it OK with you if I leave?
“Are you all right with my leave?” – Are my plans to take time off OK with you?
For me, “Are you all right with my leaving?” does not seem terribly natural. There is a mismatch between informal “all right” and formal “my leaving”. Something like “Is it OK if I leave?” would be more usual.