I'm pretty sure no passives proc spellvamp. Only abilities.
Akali.
I just don't think nashor's is that great for her. Maybe as a vanity item but otherwise no.
I've been running with ~8% cdr, and haven't had any issues. Her two biggest skills don't need cdr (Q and R), so it'd be mainly for your shield and slow. But just getting straight up AP for the shield would be better.
As the attack speed... like I said I rarely find myself just smacking on someone alot. Maybe 2-3 swipes between the combos. Not sure how much more damage nashor's would really buy you. I think heavy ap is better, since it ups your damage and survivabily, and makes it so when your 3rd strike does hit.. it hits like a truck. Like I said... if her passive procs spell vamp, but don't think it does. I never noticed it doing it when I bought a WoTA. Overall I don't think lifesteal/spell vamp is that great for her since she already has her shield. Would be a different story if her passive did... but that thing is already WTF strong already.
Thinking Rabadon, Sorc Boots, Lichbane will be her core items for sure. Secondaries Abyssal, Rylais, Guardian Angel.
Nashor's tooth isn't a good item in general imo. Same with that other item... uh... Malady.
Anyway, I think despite her kit, Diana works much better as a bruiser. She has the stats for it mid game as long as you build it probably and she can constantly proc her passive.