When you're in a party, you can limit everyones levels to the same one, if you don't then you get the exp you would get from the highest level guy. This is called level sync.
A linkshell has nothing to do with exp. It's just basically a group of people you can talk to, ask for help, do events with etc.
For jobs, you can start as one of six jobs; White Mage, Red Mage, Black Mage, Theif, Monk or Warrior. Then once you get to level 30, you can do quests to unlock a further 20 or so jobs. You can switch between any of the six starting jobs or any you've unlocked at any time from a residential area in one of the cities. When you get to level 18, you do a quest to get a subjob which enables you to use another job at the same time for half the level of you're current job. So, if you are a level 60 Dragoon and you want to sub Samurai, the Samurai will be at level 30 (if you've leveled it that high) and you get stats boosts and abilities corresponding to that level, so for subbing Samurai you would get boost plus Hasso, Saigan, Meditate etc. You use gear to polish up your stats too, basically like most other RPGs in that sense.
