Holding down the left arrow key at the very beginning of the level results in Juni not falling down the well at all, and being able to "win" without seeing more than the first screen. (It's
not possible to do this by holding down the
right arrow key, so the best way to fix it is probably just widening the tunnel mouth by one tile. Just don't forget to adjust the next screen down accordingly, so you don't wind up with a wallswim.)
Also, it's possible to stand on top of the tree-house on the screen with the sitting man. Or did you put that tile on level 3 intentionally?
I think you used a flag warp to send Juni to the version of the third-gate screen where the gate is open? (This is the screen above the eye I'm talking about.) When entering the screen from the left -- though not, oddly, when entering from below -- I can see the closed gate for a split second before the warp kicks in.
The pale-red diagonal background tiles on the right side of the cavern (but not the ones on the left side) are on layer 3.