1.Best way to get gils ? Gathering is a good way?
Gathering is one of the way to get gils, combined with crafting you can earn more. There are alot of ways to get gils in this game but the two I mentioned are easy to start with.

2.To buy the game it only costs 9.99 with 30 days of time included?
When you buy the full game, you get 30 days of non-trial game time (iirc it doesn't count towards veteran reward). After the 30days, you need to find a payment method convenient to you to start the actual subscription.

3.Today i discovered i can talk to a class guild and change my class. This works like i start from the beginning and level up the new class with the same quests?
Whatever Main Scenario Quest that you progressed through retains with the character so you continue where you last left off. You just start leveling with the new class from level 1 again (level 30 for expansion jobs) and get new different set of quests associated with the class/job.