To progress in party content (including the dungeons required by the main story) much past level 30, you're going to need to unlock job(s) for your class(es). Conjurer just isn't a good enough healer, Gladiator isn't a good enough tank, etc. Unlocking a given job requires a specific combination of classes leveled. The jobs are also limited as to which classes they can pull cross-class skills from. WHM can only use skills from ACN and THM, for example.

It may help to not think of the jobs as class 1 + class 2, since they don't really play that way. A WHM isn't so much CNJ+ACN as just specialized CNJ. The WHM job quest just has a requirement of having ACN to 15, and you can pull skills from ACN. But you don't really add in play style elements from ACN.

When you're soloing, you can stay as the class(es) and cross-class whatever skills you want. If you want to be a Conjurer with a bunch of Archer skills when you solo, that's up to you. Some of those skills will be helpful, some will not. Hawk's Eye, for example, won't do much good, since a CNJ doesn't get much use out of DEX or physical accuracy.

Eventually, they're going to include a salon feature that will let you change your hair style, tattoos, etc. Not your race or gender. I don't know if they've given a specific list of what it will let you change. Until then, the only way to change anything (and even after, the only way to change race or gender) is with a Phantasia potion, which you get as a reward for your first 30 days of paid subscription time.

Couerl mount is a reward for the Collector's Edition. Legacy Chocobo mount is a reward for having an account with Legacy status. Ahriman mount is a reward for 90 days of paid subscription time. Unicorn is a reward for the level 30 CNJ class quest. Magitek is a reward for completing the main story quest line.