When I explain something to my friend and I want to make sure they got what I said, what should I say?
- "Do you understand?"
- "Did you understand?"
- "Have you understood?"
Any of the examples you provided would work, but note that they could appear condescending depending on the context - like you were speaking to your friend as if you were expecting him not to understand at all.
Something more informal and deferential, at least in the United States, would be did you get all of that? or can I make anything more clear?
Any of these. Colloquially, the question is most commonly
and the reply
You can also ask
and this has a slightly different connotation from "Understand?", but I'm struggling to work out what the difference is. I'll come back and edit this if I work it out.