Character/job level questions (spoilers)

[Rez09]

It's a bit late, but, as I recall, Monks have no access to white magic, or magic of any kind really. There is always the option of potions if you need healing, but at the point you mentioned I don't think you'll be too bad off without white magic. Monks should deal enough damage to kill things off for you before they are much of a threat. Also, you can keep your eye on your xp and swap your mages to the monk class before you level. You'll lose your remaining spell charges, which is a headache, but it'll give you more max hp for the earlier sections of the game. Later on my experience with the remake is more limited, but in the NES game I swapped my mages to the Warlock/Magus class, which had better HP growth and still let me use black magic, for clearing mobs in the Bahamut cave for xp.

As for gearing out your monk better, just go bare fists after Nepto's shrine. You'll score a lot of hits and being unarmed always counts as having two weapons, so you'll get more damage too.

For leveling classes, some classes will gain job levels faster than others, and their progress is based on how many and what actions they completed in battle. Job specific commands, as Kanno mentioned, do give more class xp towards the next job level, but one can usually defend (or use another non-attacking option) ten-ish times in battle before ending it for a guaranteed job level. This rate falls off after a certain point, so you have to defend/idle more times, but the method will work until you max out the job level.

Hope that was helpful in at least some measure.