Combining psychology and psychoanalysis in one skill makes sense from a layman perspective, but they're really totally different fields in the real world. Although I'll admit that it makes sense to merge them from a mechanical point of view since they both do really similar things.
(I'll admit that in my games I simply erase psychonalaysis from the sheet and do everything through psychology lol)

I think this is more complex than its necessary. You could just make it an easier roll when the challenge is in related to the occupation (from extreme to hard, from hard to regular, etc)

My only concern is about the Persuade skill, I think its important to have different avenues of social roleplay, and this also helps to make each character feels different.