1. PS is a class-less game. There are no classes and no predefined jobs. You create a character of a race of your choice, and tweak the initial stats to your liking. From there, you can do anything you'd like (that is currently in-game, of course).
2. There is one free-for-all PvP arena at the moment. PlaneShift is a PvE game more than PvP though, so while you can challenge others to duels outside the arena, that is definitely not one of the main activities of the game.
3. There are no mounts yet, but they are planned for future releases.
4. No levels either :) You train stats and skills to progress your character.
Take a look around the main website, as well as some threads marked "Important" in the forum. They will help you learn more, as well as answer any further questions you might have.
Welcome to PS!