1) Your test answer is correct. It matches tense with the question.
2) "I know her since. . ." is not grammatical. The simple present is not used to encompass a period of past time.
3) Present perfect "have known" is exactly the right tense to express something continuing from the past up to the present moment. "Had [verb]" (past perfect) is used for past {event/situation} which {completed/is no longer the case}.
BUT "know" is a special case, semantically unlike other verbs (e.g. support, date, sleep with—see #5.)
4) "How long do you know her?" is not grammatical (see #2.) So it makes no sense to ask whether this means something different.
5) Yes, one might ask "How long did you know her?", but it does NOT mean you don't know her now, BECAUSE once you "know" her, you cannot later not know her. (You could have a falling-out; you might not see her for 20 years, but you still know her.)
So, "How long had you known her" would be asked in reference to a particular moment in the past:
- How long had you known her when you first kissed her? "For a month".
And "How long did you know her" would be asked in reference to a certain period in the past:
- How long did you know her before you were engaged? "Eight months."
... but both of the above assume that the "knowing" continues now, and into the future.