I vaguely remember a "robot fight arena" style game with a similar premise, except as an async PvP with an if/then style programming language. It had a solid fan base back in the day.
I would have kept playing after the tutorial. The just-in-time skill unlocking makes it hard to assess if I'd have buy in starting a fight with a batch of already unlocked skills - as the prototype exists, by the time the player understands the UI and finishes the tutorial there's nothing left to test against, so I can't say for certain if I'd enjoy the game proper.
The first three questions you list are all "No"s for me, but probably just because the tutorial held my hand until the last seconds of the game. I'm afraid from a new player's POV this is more of a prototype of the tutorial than of the actual game system itself.
Using a phone, I had to choose between watching the combat log or seeing the rotations - both wouldn't display at the same time. If you like the "Rotation" term, maybe making the actions play out via overlapping circles, like clocks imbedded in clocks, would condense the UI enough to present both simultaneously?