Did the second dungeon, got to the third. No key. Went back toi second and checked the boss draugr's body but must have picked it up. Possible I dropped it or sold it by mistake? I don't remember because i was playing with a belly full of mead - well, Happoushu anyway. Can't get into saarthal now...

I may be wrong, but I think you have to join the college. Pretty early on you are taken there and they open it for you.

Speaking of which there's this horrible woman who tries to kill me at the college gates. How do i get chummy with her?

One of the infinite wisdoms in Beths design descision, you have to join the college to get in.