Is the entrance fee for the actual mansion, or can you walk around the grounds for free? Or do I have to pay?

You have to pay to walk the grounds

You have to pay to enter. They give you a wrist band.

Water temple in san Carlos

Annie and Cathy are correct.

You pay at the main building. After that the mansion is no extra charge. You can purchase a membership too.

I think you can go to the gift shop & dining room without a ticket, but you do need a ticket or membership to visit the house.