Assuming you don't have bonus experience buff, your level will be in par to the story, so I recommend to run the little quests to get extra gears and/or to maintain level. In case your level overpower the storyline, then no need to run them. BUT, there maybe some things (like materia melding) that get unlocked from the side quests..

Level will not reset to 0 if you leave the game and return after expansion. I guess you created new account hence your other classes are 0.

Stick to the main story first and enjoy the story. Don't worry too much about end game content as you will unlock them sooner or later. Most of the interesting stuffs only start when you reach lv70.. So focus on achieving that first

Also crafting is hard if you haven't unlock all area because you will lack in materials and gils to level up those classes..

https://eu.finalfantasyxiv.com/lodestone/playguide/
In this link you can find some game features that can be unlocked..