It is fairly clear what that means. So, no. It is not ambiguous. It is not likely to cause any confusion.I don't know many things about her.
In (1) don't is stressed (slightly). In (a) not is stressed (slightly), and few is stressed (more strongly). In (b) many is stressed (as you suggested).1-I don't know many things about her.
a-It is not true that I know many things about her. I know few things about her.
b-There are many things about her that I don't know (may-be there are also many things about her I do know).
[If I am correct, in spoken language the difference would be clear. I think in a, don't would be stressed and in b many.]
I think you have got it just right. :D
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