"Quiet, please." (On a sign, for example.)
Yes, that is also acceptable.
Cannot "please be quiet" do?
I tried the same, rejected. Hope a native Chinese speaker could comment on this.
Would 'Please remain quiet' be accepted as well?
"Please be quiet" should be accepted... you ask people to "be quiet" not to "keep quiet".
How about "Please keep in silence"? Shouldn't be?
No, shouldn't be.
'In silence' is a condition, it describes something else. You can work in silence, for example. So, with 'keep' it doesn't work, as 'keep' requires an object, adverb or verb to describe, which 'in silence' isn't.
still your sentence is unnatural.
unnatural sentence... maybe you meant "please keep silence"?