Please explain Kat vs Zed match-up

I'm trying to learn Kat, I know how her kit works. She is fine for me but it's her match-ups. I'm having difficulty against melee match-ups for kat and some of you may be wondering or questioning why. My champ pool consists of ranged champions, so especially turning into a melee champion, it takes more knowledge and thinking. It's hard for me imo and I hear, Kat should be able to beat Zed, if she's good of course.

So my problem during lane versus Zed is when to engage. Do I punish him when he uses Shadow? Cause if he hits me with w-e-q, my health is obviously low and yes, this is where I should dodge, e to a minion, etc. But I like making trades, I hate being passive and anytime I go to trade, I kill myself. So.. yeah. And his ult.. I thought I had to save w to fight him in his ult, but I guess not. I was told Kat needs to save her q in order to get away or make a turn around, during Zed's ult. What do Zed mains usually wait for in order to kill Kat?

P.S. I've watched a couple of Zed vs Kat match-ups and it's unfair, considering the Kat tends to get the Zed passive player but my Zed players are aggro af.

[sg-soraka]