Did you quieten down
Why not "Have you shut up ?" - this is what we would say, as in "Have you finished ? Can I get a word in now please ?" :)
The correct English is: "Did you fall silent?" / "Did you become silent?" / "Did you become quiet?" All these should be accepted as correct. "Did you quiet down?" is not English.
"quiet down" may not be English, but "quieten down" is, and I'm afraid your other suggestions aren't really used in normal English.
"To quiet down" is an existing phrasal verb
My problem here is that what with the lack of context and the weird translations, I'm really none the wiser how these expressions are used in Romanian, who to or when.
Can you also say, "Were you quiet/silent"?
What english is this? "Did you quiet down".....
I know it's not literal but I think it would be more natural: Did you stop talking?