I went to double check and I think mage was rotating fine. I hadn't noticed there were direction text on the right at first and the sprite looked almost the same facing some directions. I think it would be nice to have indicators on the board too for which direction they're facing.
I think not allowing cancelling actions might work better if game was completely turn based, so time kind of freezes as the player makes their decisions (and even then, maybe have this be a separate hard mode, new players likely want to get more chances). But when boss and other character timers are independent of each other, so game kind of values input speed as well, then it will start to feel more frustrating.