A clever idea that is unfortunately bogged down by complex rules and unclear presentation.
The first real issue is there are too many rules and animals. I understand wanting to add depth and challenge, but the other animals should have been introduced slowly as the game progresses. Start the player with only 1 (the mouse), then 2 (Mouse and cat), then 3 (mouse, cat and snake) etc... (I think y'all already mentioned this in the comments and it's a shame that wasn't implemented!)
I think the presentation would have made a huge difference as well. If we could properly see the rooms connected to each other, it would be easier to know when something is separate or close, if we could see the animals move as well, it would add charm. Also could then use them to show if the connections were successful or not. That's another thing, it would be better if there were sfx and some animations to show the player successfully finishing a level, getting points or even losing. Like if the cat attacked the mouse if you connected next to each other.
Another thing is giving players three chances to fail. Why should we immediately lose? I think it would be more fun if a part of the space is locked out after that, and you still have to try to beat the level, with only two "lives" left.
Overall a cool idea, that sadly didn't seem have to enough time to be executed properly.