Have some people seen her?
Has/Have any of you seen her?
You go first, Frank!
Was there something hard about that which I missed?
When you chose any as the subject in #2, what motivated you to do so?
It is a pronoun -- an indefinite pronoun. Those are often missed because people only think of the personal pronouns.
Is "det." short for "determiner"? I think that is a British, not American, term.
Anyway, "any" can be an adjective or .a pronoun, and as a pronoun can combine with "-body" or "-one" or "-body else" etc.
At least this is true, using the terms I know.
You say these, Frank:
Have any of you...?
Has any of you
We both know this:"any" can combine with "-body" or "-one" or "-body else"
Has anyone (=pronoun) (of you = modifier) seen her?
With 'any' goes 'have' and with 'anyone' (any + one) goes 'has'.
Now see these again:
Have any of you seen her?
Has anyone of you seen her?
They mean the same thing; but then, the subjects, which the sentences are about, should they not be the same in the two sentences, concerning their number? Or are they the same in number, only their number-assigning properties are different?