I'd first like to note that cat isn't uniquely defined. See the image:
The meaning of this picture should be self-explanatory. Now this isn't a BIG problem since there are only two things you can try, instead of 32768 combinations or something (if there were 15 such binary ambiguities on a single image), and it will either be one or the other, but in general these things should have unique solutions. If it isn't, it should START OUT with some information filled in, to remove the ambiguity. For instance, since it turns out as by my image, the answer was "B", it could have started out with one of the "B" squares already filled in, at the beginning. Preferably the one in the lower left, since the one in the upper right would make for a very big clue at the beginning. Or maybe there could be an "X" starting out in one of the "A" positions. One or the other. That's the way it should be, so that it is uniquely defined, there should be a minimum amount of information included at the start so that it is resolved without ambiguity. I only did 3 of them. Cat, cheshire cat and winter. It's kind of a chore, and doing all of them would take some time. So I don't know what kind of ambiguities there might be in any of the other puzzles, it is possible that some of them might be way worse than a simple choice between two combinations, so you ought to watch out for that.
Another thing, when you test and solve one, it doesn't seem to me it should just say "Great! You win!". How about it shows you the completed image without the grid or all the marks you have put into it when you're done? Instead of the way it is, where you can simply never see it again, it's gone immediately.
I think armor logic 2/picross logic 2 had it right with the mechanics of marking these things, where you hold down shift to mark things as x instead of filling them in. I don't like this thing where you have to click multiple times, though you can hold it down at least. Not for marking the numbers in the rows and columns though. It ought to be so you can mark those by holding down the button. I also like the 5 strikes and you're out behavior of that, where you can get active information back with a guess, this is too much like solving it on paper.
But at least it wasn't as bad as picross logic 1, where you can't do any of the "advanced" puzzles until you've solved ALL the trivially easy ones, and where you can't mark them at all by holding down the mouse button. That was unpleasant as hell and at least you made it MODERATELY convenient compared to that.
They're nice little puzzles.