Yes your character carries over from beta.

Question 1
The entire game is cross platform and uses the same servers. the same character is available on every platform that includes PS4

Question 2
12.99$ is the fee for ONE single character per server. 14.99 is the price to have 8 characters on one server. you only need one character though, because one character can play every class

Question 3
you get 30 days free, doesnt matter which platform you buy the game on