The biggest thing I see in your gameplay is that your CS is low when you play mid and it feels like you are a little late to fights in my opinion. I don't play jungle so I don't know what good CS for jungle is so can't comment there. I watched an Ahri, Katarina, and Kha'zix game and some of the things that were odd was just how low your CS was for the time.
You want to strive to have 100 CS by 10 minutes, and in some of your games you'd have 100 in like 20 or 25 minutes. I believe it was your Katarina game where you got the entire first wave, and then got only one from the second wave. Obviously you'll miss some unless you are in a passive lane, but hopefully not that many. The Annie you were playing against in that lane was extremely passive also, so it wasn't like you were trying to dodge her poke or anything.
Another thing was rushing mobi boots on Katarina before even getting Luden's. If you had rushed Sorc boots, I could maybe understand, but Mobi's didn't make much sense. I get you were running around trying to gank other lanes, but the Sorc boots would've been much better if you were running around hoping to get kills.
Your Ahri game was almost the opposite though. You pushed your lane constantly, but never roamed bot despite the enemy lane being at your bot lane towers. Granted, your ADC in that game wasn't doing that well, but if you had wandered down earlier, you might've been able to shut the enemy ADC down before they got so fed. That game was a little weird cause they had AD TF, Kayle, and Tristana, so even if you killed one, the other two were able to carry the rest of the fight. In that game, it might've been better to split push instead of team fight. Ahri is so slippery with her ult and has great wave clear. If you had gone to a side lane and let your team play ARAM, you would've at least split up the enemy team instead of letting them group the entire game. With TF obviously splitting is a little harder, but teamfight against them didn't seem to work.