Learn English – “Defined by me” or “by I” or “by theself”

In my strong opinion, from all the above sentences the only grammatically correct is

You need your and your partner's documents.

Although I would put it:

You need your partner's and your documents.

To test it, you may take away "(and) your partner's"):

You need your documents. (correct)

*You need yours documents. (incorrect)

*You need you documents. (incorrect)

The expression

meets student needs

is correct English. They are using the word student as an adjective, as they would were they to write student guide. Although they could have alternatively written it using the genitive case as meets students' needs, it would seem that they have chosen to write it in this simpler form.