Do parents have to pay if they’re not going to any exhibits/activities in the building? As well as this, how much would a teenager cost/have to pay to enter?

Yes, there is a charge for adults as well as children. $11.95 child, 15.95 adult or teen.

If you plan on going more than once, it really is a good idea to go for a membership, I have one for the family, and the cost for the year is about what I would have spent for a single visit.

I don't think there's any way for an adult to get in with a child without paying unless you sit on a bench and just leave your kid to roam free.