1. Whenever I use my left or right arrow keys, sometimes, on medium grid, it doesn't fully go to 90 degrees after two turns (rather 89.999999999912 or something like that). It also only happens on models with a large number of pieces and this problem only happens when rotating on the y-axis.

2. Some of the angled pieces aren't exactly angled as they are named. For example, piece 32192 is suppose to be angled at 135 degrees but in the workshop, the bent angle is marked as 134.9225760415. Is this a part modeling error, or something else?

The first one is due to how computers handle floating numbers. However I am unsure how you get to see it in the object panel as default decimal number is set to 3 which iron any of these tiny inaccuracies.

I am unsure about the second one and I will check when I have a chance as the difference is not negligible. 3D models and snap points are decoupled anyway. They are defined with quaternions not Euler angles.

For the first one, I set the decimal to 10 places.

The second one also happens (albeit in placement); part 6120's only snap joint is noticeably misplaced.

Keeping 10 decimals is completely irrelevant. It is 0.1pm (picometer) which is a unit used to measure atoms...
More reading about floating point numbers

Is this also related to why, when I save a model with something rotated at 15 degrees and open it later, it props it to 14.9999909544?

yes.
I also updated point for 32192.

Hello again. Is there a way to round all the pieces in a build to a certain place? I rotated a whole model on a pivot point and when I reset it back later on all the pieces were weirdly misaligned.

Please provide a process to reproduce or even better, as short video of your screen when the issue occur.

Will images count? (computer does not support screen recording)