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

"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?"

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.

Yes. Both phrases mean that... Another way of use is simply stating them, instead of questioned. ex. "you get me" ...just like an affirmation of the fact that "you understand me", "you feel who I am", "you see what I'm about", "you see ME". Used this way, both phrases "you get me" and "you see me" acquire a bit more of a sensory-like meaning; perhaps more like a recognition of emotional understanding and synchronism rather than just the comprehension of what's verbally expressed.