Whoaaaaa picross flashbacks! Really nicely done! I loved the tone of the intro story and the way the puzzles were integrated. I didn't notice the health system at first and was confused why it filled in the right thing when I guessed wrong, but I think that was a good design choice now that I understand it, rather than letting the player make a wrong move without knowing it. It seems like a small thing but the SFX for clicking squares in the puzzles makes it feel so much better than it would have without it, especially using different ones for filled and unfilled squares, and was a super good addition.
I agree with other commenters that a little cleaner alignment of the hint numbers and a grid overlay to really lock things in would be great additions, and I did run into the same missing hint number on one of the puzzles (it was level 5 when I did it but they seem to be somewhat randomized). I'd love to revisit the game with those changes and maybe a few more levels added!
Also, from a former Fusion user, way to go making something this unique! I haven't used it in a long while but I remember getting really confused trying to do UI stuff and this works great!