Need some help understand the class/job system

[Shougun]

To become a Black Mage it will only require a level 15 Archer, however you should consider leveling Arcanist to get some of the cross class skills like Virus and Eye for an Eye (and in emergency Physick may become helpful).

Your only real restrictions to becoming a Black Mage is having 30 Thm, 15 Arc and then completing the main quest Sylph-Management. When you are a class you can use all the cross classable skills, when you go to a job you can only use the class skills your job has association with (Black mage associates with THM, ARC, and ACN).

No class will level when you are not playing as it. So playing as BLM or THM will not level ACN or ARC. You will have to level them specifically. Edit: Misread the question, Anova answered it all anyway, but yes you get an exp bonus called the Armoury bonus when you are leveling something under your highest leveled job. Please be aware certain abilities will be expected of you so be careful taking too much advantage of the Armoury bonus (for example as a white mage you are expected to have Swiftcast, you will have it for being a level 30 THM but sometime people haven't and they might receive party stress because of not having it).

You can switch between all classes and jobs freely, welcome to FFXIV .

Arcanist has Physick (lvl4), Virus (lvl12), and Eye for an Eye (lvl34)
Archer has Raging Strikes(lvl4), Hawk's Eye (lvl26), and Quelling Strikes (lvl34).