Do "You see me?" and "You get me?" mean "Do you understand what I mean?"

Solution 1:

"You get me?" most certainly means "do you understand me?" "You see me" is unfamiliar to me (US EN), perhaps they mean "Do you see what I mean?"

In any event the context you provided (question asked after an explanation) makes it almost certain that the latter question, like the other, is used to mean "Do you understand?"

Solution 2:

Rather than being used to mean "Do you understand?", in ordinary American speech the phrase "You get me?" is used as near-meaningless filler; that is, like "You know" it is a discourse particle. ("In linguistics, a discourse particle is a lexeme or particle which has no direct semantic meaning in the context of a sentence, having rather a pragmatic function: it serves to indicate the speaker's attitude, or to structure their relationship to other participants in a conversation.")

I don't recall hearing or reading "You see me" with any relation to "Do you understand?". I have heard it said (or have said it) in sentences like "You see me on the left in this picture." Of course if I heard a person say "You see me?" several times in a conversation, I would class it as a discourse particle in that person's vocabulary.