I'm thrilled you are enjoying it. It's been a labor of love to make. Well at least the 1st few years were... It did start to turn into a chore towards the end. Sadly all the puzzles are 55 tiles and there shouldn't be a time limit... At least I don't recall putting one in.
There are 3 puzzles per key item you get. We can use the cats bell as an example.
Once you get the item and complete all 3 puzzles you can then call the Neko into battle via a cool down ability.
Not to spoil things but there is more than just those puzzles. Thing will unlock as you play.
It's very helpful to unlock these. And a note to all, blocking in battles will be needed as its not a useless command.
Lastly, there are 80 of those puzzles.
~MDZ