First Impressions on Kai'Sa
I think she is an interesting champion with some versatility and unique playstyles as being an assassin/marksman/ad burst mage. I don't find her to be that useful as a jungler because her Q deals reduced damage to monsters and gets split up against multiple monster bunches and her E boost doesn't do much against them so she is forced to be a laner and probably a bot lane adc. It's sometimes hard to find the exact moment with her Q that isolates an enemy champion and her main role is to burst people down with her Q W more than the attack speed boost she gets from her E.
Her passive is fun but I am not believing the hybrid dream it was encouraging. She bursts much harder with crit ad builds than having to water her kit down with some ap because the bulk of her burst is from her Q which is physical damage and that makes it harder to penetrate people with defensive items.
Her Q is amazing in clearing waves later on in the game along with champions, the isolation thing gets annoying but it does so much damage im ok with that.
Her W is hard to land long range but short range it makes a great harassing tool or to charge up her passive to execute people and set up her ultimate.
Her E is useful for kiting because she is super slow otherwise but the attack speed boost isn't worth it that much only because she gives up auto attacking long enough to make the average attacks per second a lot lower. I guess if you dodge some skill shots and then attack a bunch it's not too bad, but it's not worth using her E while dueling if you are just right clicking something.
Her ultimate I thought at first was lackluster but I am finding it to be extremely fun and useful. You can use it to catch people who thought they got away, or even just use it for it's big shield if you are later on in the game with a large amount of ap or ad. It can be used for a lot of reasons, but because it is a pretty long enough of a CD it can't be used that effectively for ganking but can be used to turn a duel around in a quick dash.
I don't think it is realistically possible to evolve all three of her abilities only because of the high thresholds each ability has. The easiest one is to get 100 bonus AD for her Q. To get 100 AP you must really invest in her AP but that ruins her E and auto attack burst.
Her E is by far the hardest, if not impossible, to evolve because you would require 3 or 4 attack speed items You could of course build two nashor's tooths but that would be wasteful of your item slots. If you spend 4 items to get .5 seconds of invisibility, you will have a very low amount of AD or AP and your Q W R values will be so low that it will not be worth the sacrifice.
That being said, her cool passive only lets you mainly only evolve her Q, but that makes her kit still a pretty solid.
I wish her evolutions were more easily accessible because I feel like we were supposed to reach them, but the 100% attack speed cap on her E is way too high to aim for and she isn't meant to be an APC to upgrade her W.
Kai'Sa is a fun bursty semi mobile ad caster assassin but I believe her passive needs some tweaking.