Hi there,
You don't hail a taxi. Go to the taxi desks at airport arrivals where the prices are clearly posted up. Pay at the desk about 600 - 700 baht to Kata. About a one hour taxi ride.
FantaSea is billed as a Cultural Theme park. The show is really good but it's more like a cultural shopping mall. The park opens at about 18.00 for the Thia buffet meal starting about 19.00. The show starts at about 21.00 for hour & half.
Book through any travel agent in Kata and the package will include pic-up and return to your hotel. The show costs about 500 - 600 baht and for the optional the buffet then additional 400 Baht (approx price, various deals on offer through travel agents.)
Have agood holiday,
Wallee & Alex in Patong, Phuket