I don't know the answer to this question. We were there for a few hours and did not see anyone with a pet inside although did see someone with a small dog in the car park. Note that whilst there is quite a bit of outdoor walking there are several indoors museum buildings where I'd assume pets are not allowed. If you have booked a hotel already or are already staying in a Jeju hotel, I'd ask the hotel staff to call the Stone Park and find out.

You can stay at City centre hotels or Seogwipo and visit Jeju stone park. You can hire car and drive or take full day vehicle with driver on hire

There are regular buses from the Jeju Intercity Bus terminal that stop right outside the entrance to the Park. Cost is about 1,200 won and takes about 45 minutes. I can't remember the bus number, but the people at the information centre at the bus terminal will tell you!

It’s KRW$5000 for adults, KRW$3500 for children. There is also a discount for groups (more than 10 people).

You mean to spend at the park? It is a huge area. If you really read the information there, and stop for some pictures, you will at least need to spend 3 hours, to cover the whole park. I am not sure that is possible. We only covered a third of the park.

Its the real grandfathers & some routes are creepy.

Entrance fee is 5000 won for adults, 3500 for children. There is a 500 won per person discount if you book online but it's not really worth the hassle.