Zoe is so badly designed....
So let's analyse.
Zoe's passive, i'd say that's not exactly unique but it works and isn't busted, moving on.
Zoe's Q, this ability is one of the main reasons that zoe can be broken, they need to nerf the damage and the mana cost, so it can't be used so freely in lane, nor to one shot someone with one q.
Zoe's W, this is completely crap design, putting rng into a game like league is pointless and would never work.
Zoe's E, pretty broken but its easily fixable, just stop it being able to go through walls. thats just dumb.
Zoe's R, its a nice idea but badly implemented.