There are many steps inside the actual cave, there is a ramp down but you can't go far into the cave with the stroller wheels down. You can bring it into the shop though, if that's what you want to do.
No it is not advised. There are steps and the cavern is still active so there are wet spots that can be slick. I advice using a backpack carrier for children. I hope this helps!!!
Alot of steps, not recommended
Not unless you want to carry it and the baby the whole tour. I agree with Jeff. The backpack carrier would be best. Have fun.
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