Job question

[Umo]

One more, shouldn't my other character show up on the Classes tab on my new alt?

You're misunderstanding the Armoury System. You don't need an alt in order to level any and each class/job up. You actually level them up on your main character.
In order to unlock Scholar you don't have to level an arcanist, but level arcanist up on your character instead (see the difference?).
Get your main character to the arcanists' guild @ Limsa Lominsa and join the guild. Equip the weapon you're given by the guildmaster and BAM! now you're an arcanist. Your progress as a Conjurer is saved and you can change back just by equipping your Conjurer's arm. Once you reach arcanist level 30 you can unlock scholar because you have already level up Conjurer to 15.