Welcome to Eorzea!

1) There is a quest north of Black Brush in Central Thanalan that gives you the Convert ability. There are actually several quests but the others are related to melding materia and require crafting classes.

2) There is no point in getting one class to 50 before switching. Switching is generally encouraged because of the cross-class skills. And you will get flak if you are trying to run high level dungeons as a gladiator instead of a paladin. :/ The 50% bonus xp is for all classes below your highest - so it is better to keep one ahead of the others, but you only need 1 level ahead.

3) Crafting is widely debated. The only benefit in getting a crafting class to 50 is the same as for all other classes - cross-class skills, level 50 equipment, and access to more recipes. I would say there isn't much point in only grinding a single crafting class up to 50 unless you are using it yourself because the really high level recipes pretty much require cross-class skills. That said, crafting is a good way to get yourself gear while leveling. You can make high quality gear that is better than store bought and basically equivalent to dungeon drops. Those really high level recipes can also make level 70 gear for giving you a jump into the end dungeons, if you prefer crafting to running dungeons.
Of note: if you want to attach materia to equipment, you will need the services of a crafter. For your relic you need a level 50 crafter. You will most certainly be able to find one if needed but I like being able to do it for myself.