The basic (declarative) sentence is:
He does not know.
You can turn this into an interrogative clause with subject-auxiliary inversion. Just switch he and does:
Does he not know?
You can optionally replace does not with doesn't in the original sentence, using the suffix -n't rather than the word not:
He doesn't know.
Now the auxiliary is the single word doesn't, so if we apply subject-auxiliary inversion, we get:
Doesn't he know?
Lastly, you can turn the original sentence into a question by using rising intonation at the end, which you indicate in writing by replacing the period . with a question mark ?:
He does not know?
However, this is only appropriate in certain situations, for example as an echo question—repeating what you heard as a question to express incredulity or to confirm that you heard the speaker correctly. Most (but not all) situations where this would be appropriate are informal, and as a result "He does not know?" sounds somewhat unusual. Instead, you can use the contracted form:
He doesn't know?
But most of the time the interrogative form is more appropriate.
Best Answer
Inactive is better. This is not a grammar point, but a matter of style.
Using "not" introduces an ambiguity, as it could be taken to mean "... will not remain active", a"different meaning entirely. In such a sentence using "remain not [adjective]" is rarely the best way to say something.
Say "remain inactive" instead of "remain not active". Say "remain unhappy" instead of remain not happy". If the adjective doesn't have a negation you may rephrase: Instead of "remain not red" say "still hasn't turned red" (or something similar depending on the exact meaning)