Answer 1

That's an intriguing question given that a touchscreen is 2 dimensional. And of course my coding skills are nowhere near yours but maybe one suggestion:
touching the screen with another finger could affect the Z axis.

I have seen something similiar implemented in music software, Soniface. I believe the second touch affected the Z axis (depending on how the patch is configured) when the finger moves up or down which makes sense as that software supports multi - touch and can be "played" with both hands. There are videos on YouTube.

How you could choose to implement that, I have no idea as obviously I don't know the ultimate objective.

For single finger only, possibly confine X to respond primarily to true horizontal movements (270 or 90°), Y respond to only true vertical, and any movement outside of essentially 0 (360), 90, 180, or 270° would result in rotation on the Z axis.

And alternatively perhaps the gyroscope option for Z could be considered for mobile devices.

Answer 2

Hi Mirielle for rotation there is the Euler angle what is used to denote the rotation of an object in an static reference system but if it's still.
https://en.m.wikipedia.org/wiki/File:Eulerangles.svg

Also there is the possibility to use spatial Rotation which seems to be what you need because I understand that your object is rotating?
https://en.m.wikipedia.org/wiki/Quaternions_and_spatial_rotation