is there a cost to visit the statue of liberty?

Yes

Yes.. the ticket costs 18.5$ to and fro. The ticket includes ellis island and statue of liberty.

Yes, there is. You can buy them online. The price ranges from $20 to $30 based on your option of visiting just the island or till the pedestal or crown access of the statue.

Yes there is...boat ticket.

For the tour yes

I went on a group tour, yes I paid the tour company.