Firstly, I'll clarify for posterity:
1. There is a fixed number of "control turns," and you'll run out of control upon using them up.
2. When you run out of control turns, the character moves on its own with a simple A.I. (that can also jump, unlike your manual control).
3. The 2 ways to win are (a) manually get the coin & flag while in control or (b) set the orientation up correctly on the exact turn you run out of control to allow the A.I. to succeed.
Once you figure it out, it becomes a cute and fairly engaging puzzle game. Quite clever, but it needs better descriptions or a starting demonstration/tutorial to convey the core mechanic of intentionally running out of control. If I hadn't stumbled upon the mechanism while trying out different levels at random, I would have thought it was all a buggy implementation. Fortunately, I discovered the mechanic (by chance, mind you) because the game was quite fun once I did.
The puzzles are well done. Going through them in sequence, some help introduce new mechanisms (subtly), while a few others feature puzzle designs that subvert your expectations. And for the record, I beat it. So yes, all levels have a valid solution.
In addition to properly teaching the player the main mechanic, it could use some more levels and perhaps an easter egg or two. But overall, it's a very good showing with a good mix & balance of elements. ...And yes, it is very cute. Cheers to the devs!
Good work.