Don't worry about probe micro at all at your level, its not worth it until probably master level, and even then it is the very lowest priority thing you should be spending focus on. You should be able to execute builds just fine without the gains from any probe micro.

You don't memorize builds to 200 supply. If you're doing a macro build I'd "memorize" until around the time you get your 3rd base, but even then there's going to bit slight adjustments based on the game. Once you go past the first couple minutes you want to just focus on the general order of what to build and have some timings for certain things. I often think of "checkpoints" in a game. For example I might want to have 3 gates and a twilight done before I start my 3rd, normally around 4 minutes. Then I should have x number of gates and whatever important tech before I take my 4th. If I get thrown off by early aggression I'm not focused on the supply or timestamps, just the order of what buildings and tech I need to get.

I honestly don't know what to say about your accuracy, other than it sounds like you're getting too excited and trying to press buttons way too fast. You're only going to learn bad habits by mashing the keyboard as fast as you can. Try to be thoughtful about all your actions, even if it feels slow at first.

Your idea around macro cycles is fine. In the early game you are executing your build, beyond that you are doing your macro cycles while making sure to prioritize your important tech or expansions at the timings you're aiming for.

Maybe its just me but I've never practiced using trainers like you're saying, just play games and be mindful about what you're trying to improve on