1. Levels aren't as important as skills, see below.
2. Stats increase with levels, but not at a fast pace. You will get a boost to speed and attack as you level, but mostly what is increased is HP and MP. Thus, having high levels isn't nearly as important as having good skills. Having high levels is simply a bi-product of having good skills.
3. Job levels are limited to level 8, and the only jobs that really require anything close to that to unlock are jobs like the Calculator and the Mime. Most jobs can be unlocked with a 3 or 4 in all other jobs. Aside from boosting the amount of JP gained with each action and unlocking new jobs, that is all the job level does.
4. As was said earlier, that's faith-based. Raising Brave and Faith are good ways to increase your attack (Brave) and magic attack (Faith) damage outside of leveling. Be warned, characters with a permanent Brave of 5 or less or characters with a permanent Faith of 95 or more will leave the party permanently. Ramza is exempt from this rule.