Kunoichi: Ah, that case I would want keep my cohort instead. My bad misreading the feat then. But I do also like having +2 bonus to my four skills for having apprentice, so can I keep the bonuses even if my apprentice graduated and became my cohort? If I do continue give her lessons 8 hours per day the bonuses would stay right?
Anyways here comes my char in below. According the DMG II regarding how high level my mentor is, he is 10th level (or 11th if assume I was LE when I started studies as apprentice but later moved to neutral evil and it does not affect mentor's level after taking the feat).
The +2 competence bonus comes from taking the Mentor feat, so if you're taking Leadership instead, you wouldn't get the bonus. Though, since your followers from Leadership don't gain levels, if you have both Leadership and Mentor you could easily have one or more of them have the Apprentice feat and get the bonus that way. Of course, since it's a competence bonus, it won't stack with most skill-boosting items...
As for your Mentor, the only real requirement for him is that he be 5th level at minimum, to qualify for the Mentor feat. Aside from that, he's an NPC and only gains levels when the DM decides he does.
I decided my mentor (when I was apprentice) is Samas Kul, zulkir of transmutation. Considering he is 15th level I assume it's okay so long he does not give me 6th level or higher spells copied for free from his spellbook. Now so far as I understand the apprentice feat for wizards it means I can copy higher level spells from mentor's spellbook instead just getting spells which are appropriate for my level. So example in 2th level I could copy from master's book a 4th level spell and so forth.
Considering Thayan culture, I think your Mentor would probably be specialized in the same school of magic that you are. The political hierarchy is pretty heavily divided between the eight different schools of magic in Thay, and the Zulkirs in particular are at the top of each respective faction, so I doubt that Samas Kul would even deign to teach magic to a student who was planning to specialize in a school other than Transmutation. And if that student was also planning to stop studying Transmutation altogether in order to more closely devote himself to another school when he became a Red Wizard...
Yeah, I really don't think that Samas Kul would work as a mentor. ^^; Perhaps your mentor could be Dmitra Flass
Rhaza Ankhemon was born to family of farmers. In their ancestry there has not been great mages or such but the family was wealthy enough to buy books for reading and had slaves working on fields so family lived in comfort (and continues do so today).
However when red wizard visited to test family's two children, Rhaza and Gehennora, they both showed great potential for magic. Naturally parents were overjoyed for it, but also saddened as they will now loose their children as red wizard who intents train them buys children off them and they are not raised nor meet parents until they graduate. If they wish meet their commoner parents at all that is once they have ascended to ranks of red wizards.
Rhaza and Gehennora was moved to two different masters but they were old enough and skilled enough to write for each other, red wizards did not forbid writing letters after all. Rhaza lived in Bezantur, city of thousand temples and also one dealing exports to foreign trade and importing it's main goods; slaves from elsewhere. During the market day there was on sale a pretty but very much beaten and abused halfling, Rhaza did not feel sympathy for her but he had curiosity towards halfling species at the time and on their language. So he bought her and he then trained her. Over the years he grow fond of her, like a delicate rare pet which he grooms and praises when successful and crops when it misbehaves or does not perform well when she is capable doing so. He does not punish failures if they are pushing her on the limits. Also she is regular target for enlarge person spell for the all obvious reasons in bedroom side.....once she suggested him trying smaller size she regretted uttering even hint Rhaza becoming lesser being.
He used various methods in training and discipline her, she was just mere child but he had access to resources for good trainers and she became very well trained indeed, more so as she bonded to one mage bred experimental tigers which she started use as mount and practice archery. So besides being pleasure slave she served as also Rhaza's bodyguard.
Also in city of temples he got in contact with Shar cult through one sexual orgy which was ran by Loviatar cultists....a cooperative ceremony between Shar worshippers and whip mistresses to both celebrate pain and also alleviate sorrow and express hatred. Rhaza was not drawn by Shar's doghma but more by shadow weave magic what cultists employed....he was quite tempted to learn use said magic so he formed contact to the cult through her.
Rhaza studied and spend much time indoors, he hated traveling as he had accursed motion sickness which he had suffered entire life. Even teleportation causes it for brief time. He was excellent and bright student and very cunning and persuasive indeed. Also he studied ancient lores and ancient magics of Netherese and even other non-human race in origin. He studied much about transmutation magic from his mentor, Samas Kul, Zulkir of Transmutation. But when he graduated and then became red wizard he forsworn further studies of transmutation! Saying that 'I have learned all useful things from that school and thus it holds no longer mysteries useful to my future. If I need use something I can use magic item to duplicate it.' Naturally his mentor was furious for this but it no longer mattered; Rhaza was graduate and thus independent red wizard.
He immediately formed contact with his sister and met her first time face to face for over ten years. As she has keen business skills and interests Rhaza benefits living with her for now while he provides her support when she has needs for his talents or spells. Although Rhaza chastises her for lack of grander ambitions than he. Rhaza did not contact his parents nor his younger brother who apparently had born after he and his sister had left. He thinks he is above them and thus it's below for him associate with his humble beginnings.
Rhaza after graduation learned to use shadow weave but before he is indoctrinated deeper to the cult (and it's precious delicious secrets) he had to train a apprentice himself, not wizard but a cleric and teach her about lore what he had studied as wizard and especially about magic. So he took her in and taught her what he knew. Growing close in process as they both had passion for learning more knowledge, sometimes learn just sheer joy of expanding one's knowledge. It's not love, but more a respect between them and also simple lust.
Important note about Thay's population: From what I've read, in Thay, there are two major ethnic groups. The Mulan are the nobility, descendants of the original chunk of the Mulhorandi Empire that rebelled against their oppressive god-kings and used wizardry to establish the nation of Thay, and the Rashemi are the common folk, the farmers and lesser merchants and such.
In Thay, only the nobles are allowed to learn the art of magic, though some commoners do get trained in secret if they prove to be particularly talented. Even then, they generally don't get to be Red Wizards, though. Assuming Ruby is alright with that general backstory, you might want to change it so that the two of you are landless nobles, coming from a family that hit hard times and now has a title and some money, but little else to their name. Your character could have a disdain for his family due to viewing them as parasites who want to leech off of the success he's found, rather than merely seeing himself as being above them.
Edit: Or the two of you could come from a family of landowners, who primarily make their living leasing out the land that they own to common farmers and make a nice profit off of the rent. That would pretty much let you keep your backstory as it is, with no major changes needed.
As for my character, Rima, the basic backstory I've come up with for her is that she was born and raised in a small community in the Hordelands that was formed from escaped slaves who managed to make it across the Thayan borders. Said community was raided by slavers when she was fairly young, and she was captured as part of that raid. Once the slavers joined up with a larger caravan to transport their humanoid cargo to a Thayan market, the Orcs guarding the caravan got it into their heads that it would be great fun to toss one of the smaller, scrawnier slaves into the pen of a large, exotic tiger that another merchant was carrying, and watch the beast tear the slave apart.
Unexpectedly, however, the great beast took a liking to Rima, to the point that it became extremely unruly whenever she was kept away from it for long periods of time. Ultimately, the halfling was broken in and then sold alongside the tiger as a pair, the two of them both to be kept as exotic pets, bodyguards, and for... other forms of entertainment.