This is a surprisingly complex game that looks cute and innocent on the surface, and it took me more than 3-4 rounds before I fully knew what was even happening on screen. But once you understand it makes much more sense, and one can finally have fun with it. This reminds me of Backpack Hero, where items synergised with other items by placement alone, which is a really cool system, but is very hard to balance and test. Well done!
For some criticisms, I think due to the complexity, there should really be a good tutorial on what each mechanic works and how the game plays. Directly throwing the player into the shop screen and a standard battle would make the player super confused about the game and harm the overall experience. I would also suggest adding some animations/particle effects that indicate effects like attack, heal, buffing, etc, that happen in a particular square would be nice too.
Anyway, with how complex the game is, I am surprised that you all even pull this off with the amount of time we all got in the first place. Well done!