Overall this champ feels very weak and offers little to the team. He is a liability. His only strong point is that he is fun to play, but if it's for anything competitive, you wouldn't dream of using Zed to win.
Passive
10 second cool down makes it useless for fighting. On top of that, it is reduced by magic resist. The only use I find is for last hitting minions easier. Maybe remove the CD so he can actually ASSASSINATE those low health leftovers.
Shuriken
Just a ridiculous amount of energy for a low damage poke. It's almost made purposely so you can't use it during a fight without making yourself essentially silenced.
Living Shadow
His most important skill. You have to ask yourself, what is the use of this skill? Is it:
a) gap closer
b) faster jungling tool
c) escape
d) something to add damage to his Q to make him needlessly more difficult to play
with its current range, I would say it definitely cannot be (a) or (c). The range on this ability needs to go way up to accomplish either of those.
Shadow Slash
His only good ability right now, but why doesn't overlapping living shadows deal any damage from this ability?
Death Mark
An assassin needs to have a low cool down on their ult, like Katarina or Dianna, so the player will not hesitate to use it to chase down and ASSASSINATE individual enemies. When you put a long 2 minute cool down, you are saying that it is a game changing ult, like a Kennen ult. This doesn’t make any sense on Zed. The cool down should be cut in half of its current value. It would also be good if it reset on a kill.