One really helpful tip for me when I was learning Zed was to immediately proc R to teleport behind them in a 1v1 once you set your deathmark the first time. It's a good way to get the other person to miss their skillshot(s) since you'd be blinking right behind them. I usually only hold it anymore if I'm trying to juke someone in a gank or something.
Also Jayce adc blows.