In fact for the babies growing up, I was trying to find how to make them evolve. They are babies, they are supposed to grow. For now they boost your pet (only 3 of them though) and most of them are just jumping around your home.
First, I want to add an option to merge two slimes together to upgrade their stats, so that the oldest ones are not irrelevant. This would cost some resources. And I think there should be a limit on the number of babies you can have at home at the same time.
Second, I wanted to make them grow at some point but was not sure how. Maybe after they reach a threshold of stats or if you find or create a home in a deeper level. One of the babies could grow up and be the parent, you could also choose a new pet ;).