From what I can see, I've noticed a trend regarding the amount of time your NPC stays with you. I will test tomorrow to confirm.
It seems that the length of time your NPC stays with you is based on the number of battles, not a variable amount of time, and this number seems to be 15 fights. I'll try several times to confirm. The first time I summoned my NPC, she stayed for 45 minutes as a temporary replacement for a person who had to leave for an hour. The second and third times I used my NPC, she stayed for a considerably shorter length of time. I did not count the number of battles as this did not seem important. Each time, she switched gear (though I loved what she was wearing the second time I summoned her. ^^).
I've heard that also, as long as your NPC's level would make an enemy con as being easy prey or higher, they will gain experience whether you get experience or not. I'll continue testing to confirm this as well, as well as ask around.
Personality types appear to be governed by the NPC's name and hair type (hair color does not seem to affect anything, and as for race, the personalities seem to be spread amongst them, but can be the same personality from once race to another). I will do more testing to confirm, as a friend of mine has picked the same name for their NPC as I have.
The base "job" seems to be Warrior (Confirmed: Provoke, Double Attack, Red Lotus Blade WS), and the different combat styles may determine what your NPC uses as a subjob. Naturally, for the "Healer" combat style, it appears to be White Mage. I will do more testing on this. Attacker may have Samurai subbed, as the NPC seems more Weapon Skill oriented and uses Weapon Skills more frequently than in the regular "Shield" combat style.
More updates as I find more information.