Question, i created a conjurer and i don't get XP for killing random bugs/animals around New Gridania, is that normal? It's taking ages to reach level five, so stupid.
You do get exp for killing things, but it is very, very little. This is true for all classes.
In order to level up, you need to do quests, hunting log, FATEs, guildleves, or dungeons. Or any combination of the above. Just doing the first few entries on your hunting log will get you to level 5 in a matter of minutes. Once when leveling up an alt, my brother got from level 1 to level 5 in a single uninterrupted chain of fighting that lasted two minutes all thanks to the hunting log. The early levels should fly by. Getting from 10 to 15 is the first real leveling hump to get over, but Guildleves and FATEs should get you there just fine.
Just doing the story quests and surrounding normal quests is enough to get you to level 15 without trouble for your first class. I had so many quests left over from my first class that I was able to do quite a bit of questing when leveling my alternate class (since I did a lot of dungeons and FATEs as well, originally).