1) There are many ways of leveling besides quests: running dungeons, Levequests (repeatable quests) and FATEs, Challenge Log objectives... It certainly feels more PRODUCTIVE with doing quests because the other methods can be a bit grindy, but they are there for aiding in leveling all jobs. Usually there are enough quests from each city state to help in leveling at least one job up to end game.

2) You cannot really be friends in-game cross-server. although it is possible to party with them using duty finder. (My brother plays on Lamia, I play on Brynhildr, and once I randomly partied with someone from his free company via Duty Finder) However they do also have to be in the same Data Center, as different Data Centers are not mixed I believe.