Monday is the only day that the train doesn't connect them because they perform scheduled maintenance. It is $22 for three with the train ride if you are from out of state.
They are not all connected. The aquarium and Botanical gardens are next to each other. There is a train that runs Tuesday through Sunday between the parks. You can get a pass for all 3 plus the train for $22.
You can take a train to get to all 3 from the Zoo not sure when the train runs though cause it wasn't running when I was just there on Monday.
Thanks! Your answer is awaiting moderation.