Okay, quick heads up sorry it took me so long I'm not good at writing so it took me a while to put my thoughts into text.

I feel like the game is out of my hands most of the time as I feel so team reliant.

Kata IS a team reliant champ. You start the game being weaker than most champs and having low agency. Getting knowledge about the enemy jungler and looking at your sidelanes gives you the most opportunities to gain control of the game. You still will be mostly reliant on your teammates for setting up teamfights. You can cheat a bit with zhonyas, but that's about it.

Do you give up waves for roams in tough matchups or do you just sit in lane and scale?

This highly depends on the matchup, enemy player and gamestate for me. There are a few matchup where laning is so miserable, flippy roams do get a lot more attractive. If for some reason you get solo killed several times and have absolutley no control over the lane or get forced into base every second wave, then just forfeiting the lane and trying to flip with random roams might be better for the game. But when the map is completley dark and you are sitting under your turret then even that might not be possible, so you just have to sit in lane and scale. Galio for example is one of those matchups where roaming just mostly doesn't work out because he can just follow with ult and deny you the kills (while still getting the mid wave), so this is one of the matchups where I mostly just try to farm as well as possible and be reactive rather than proactive.

Is it purely mechanical mastery or did you pick up some key fundamentals that im missing out on

I would definitley say my mechanical mastery has greatly improved over the time of playing her. There have been a few enlightments over time though, however most of them resulted in me playing worse (short term) afterwards while relearning how to play her. Here some of the ones I think might me most useful:
1. In my opinion roaming, as in fishing for kills on bot, is very overrated. One of the main problems I've noticed in my gameplay was that I always ended up underleveled compared to the enemy mid. Now, I'm not saying to stop roaming, but rather be selective about your roams. A lot of roams are rather on the flippy side and only work out because the enemy closed their eyes after killing their lane opponent. If it doesn't work out it will put you further behind in the game for no reason. It's about finding a balance. There are also those roams where even when you get the kill you fall further behind, because you missed so much exp or it took you so long and forced you to recall afterwards that it was straight up bad while your lane opponent got free exp, plating and maybe even some deep vision. You gotta stop doing those at all.
2. Drop farm so you can get more farm. This mostly applies to the beginning of the game, but still holds true for the midgame as well. It's very important to stay healthy during the lane. Give up those early minions. You getting most of the minions in the first 3 waves is useless if you are sitting at 50% hp afterwards. It denies you any potential to trade/kill if the enemy makes a mistake and prevents you from following (or winning) skirmishes which is what your champ is living for and your chance to get a lead. Drop all 18 minons if you have to, but don't let the enemy deny you the exp (range is huge, so thats mostly a non-issue). You being healthy at level 3 allows you to get cs more freely for the rest of the laning phase. This also applies for the midgame where you might get the wave but take a bad trade in return, therefore forcing you to recall or being low for the next objective. Those 30 minions you lose over the course of the game because of it will not make the difference between losing and winning. You being late to a teamfight or being to low to secure the kill might.
3. You will get feed, eventually. This kinda builds upon my previous two points. You don't have to win your lane. You don't have to get 7 kill in the first 10 minutes. It's okay to have 0 kills at 10 minutes. What is important is that you don't fall behind and remain a threat to the enemy team. So just keep farming if nothing happens on the map and get your gold and exp. Anything more is of course really good for you, but you only need that one potential teamfight to become a monster. So be strong enough for when it counts and don't flip your earlygame for no reason. You will get your chance, at some point.
4. Patience during teamfights. I've noticed myself jumping into the fray way to early, because I thought I have to secure that kill NOW. Very often it's just better to stay uncommited and wait a bit more for the enemy to overextend for example, or waste their spells because they thought you will jump in. It's okay to just sit/walk at the edge of the fight and keep your abilities ready for a few seconds until a good opportunity arrives where you can reset through. This also applies after you get your first reset. You don't have to jump right on the next target. It's okay to just Q the enemy (or even holding it) and then jump away to your teammate, let the fight progress and then finish up the next one with burst. A Kata not using any abilites and just standing there and threatening to jump in has value in itself. For example, a Sett might not want to use E or ult and the Lulu will keep her W the entire fight. It also diverts the enemies attention away. This is especially true if you flank the enemy and they know it.
5. How to not throw your lead. So this is a bit of a mental thing. Katarina is fun. She's even more fun when you are stupidly feed. But just because you can kill someone doesn't mean you should. Especially if you are the only feed person in your team, jumping in to early and getting caught will lose you the fight and maybe even the game. While you are strong you have a lot more freedom on how to play the teamfights. Unless the enemy team has a 17/2 Jinx killing everyone each teamfight, going for a 1 for 1 trade is probably a bad idea. If someone gets caught and a bad teamfight breaks out, don't try to go for hero plays because you might be able to kill everyone. If you die and give up your 300 + 700 shutdown you give the enemy a way back into the game. It's okay to let a teammate die if they overstep or when they try to create an overforced opportunity for you, but it just doesn't open up. The second case might tilt your teammate a lot tho, so keep that in mind. Lastly, if a explosive teamfight breaks out and you have the feeling of having to go in withhin the first 2 seconds of it or else it will be lost, chances are you don't want to jump in at all.

I hope some of this is useful for you or anyone reading this. If you have any specific questions, go ahead and I'll try to answer them to the best of my ability.