That's kinda just Zed being the bitch of a champ he is, one of my fav mid laners as well! What i've found is he is punishable before 6 as long as you can dodge his Q's.
◙ When his Living shadow(W) is down, that is one of the best times to poke him, as he won't be able to counter to for another 15 seconds or so.
◙ Stay behind minions as Q will do more damage to the 1st thing it hits
◙ His ult can make him un-targetable, so don't try and burn a burst ult like Syndra's/Veigar's before he ults
◙ Pay attention to his shadows!!! He can blink to them ONCE, if he uses a W and doesn't reactivate, don't be by it
◙ Before any CDR/Skill ranks, his W will allow zed 1 Q and 2 E's. If zed W-E's, don't get hit by the 1st spin, but he can use that spin AGAIN a second time before the shadow goes away
◙ If your playing an AP champ, Rush the Zhonaya's or at LEAST the Seeker's!!! As an AD Mid laner, Well, you got Ninja's you can try and use
◙ Zed will start a burst combo with W then Ults, so right as he gets out he can try for the triple E and Q, if you have flash up, that will trick some zeds up A LOT! So as he ults in, flash as he comes out of it
◙ Some champs like Fizz can avoid the Death Mark if they have an invulnerability skill. Same with zhonaya's, us it before the death mark can be put on you
◙ Dark mark will pop doing the SAME amount of damage he did before the mark pops.
◙ If Zed ults you and you see a shuriken over your head, it will pop and kill you
Hope this helps!