Welcome to the forum and the game, Branagon.
This isn't a bad thread for that, but you'll probably get more response in a new thread. Only person listening here is me.
Not having read the novels shouldn't be a problem at all. Not having read the RPG books might be. Sometimes players have trouble learning the Aspect rules, and the way stress works can be counter-intuitive for some. So you'll need to make sure people have a basic grasp on the rules before you start playing.
I think a stunt or -1 Power to use Performance for spellcasting power sounds like a fine idea. Not sure what your concern is with the focus item limit.
How to handle the full moon is up to you. Letting the player Declare it with a Fate Point sounds like a good idea.
A mortal math or physics student could be a fine PC, but they'd need some other skills beyond academics. And having two mortals with such similar abilities might be boring.
Anyway, here's a take on Achilles:
Achilles Collier (Feet In The Water)
High Concept: Former Cultist of Ares
Trouble Aspect: Filled With Regret
Other Aspects: Skilled But Inexperienced Warrior, Like A Ninja, Life-Drinking Sword, The Stubbornness Of Youth
Skills:
Great: Weapons, Conviction
Good: Athletics, Stealth
Fair: Alertness, Burglary
Average: Endurance, Deceit
Stunts:
Really Stubborn (Conviction): Use Conviction to defend against any attempt to make him back down or change his mind.
Powers:
Life-Drinking Sword [+2]
True Aim [-1]
Blood Drinker [-1]
Inhuman Recovery [-2]
The Catch (Other weapons of the cult) [+1]
Total Refresh Cost:
-2
Refresh Total:
4