No47, as someone who's spent too much time playing various versions, and follows the dev chat, but isn't a developer:
1) Programmers say alchemy isn't implemented yet.
2) All the mage does is help you control your slaves (and apparently help with training/testing girls if you're playing Maya). There's never any reason to talk to him outside the events.
3) I'm not sure I've seen a case of that myself, but girls with high enough agility can dance without the "dancer" trait, so maybe girls with too low agility can't dance even with it? In any event, you should make high agility girls without "dancer" dance, as they'll have a chance of acquiring the "dancer" trait, as well as "athletic" (good for working as whores) and "nimbleness" (sends agility through the roof; excellent for your adventuring party so they can get in first strikes in combat).
4) I think they just don't. Assigning girls to those jobs helps other girls, not the girls assigned to those jobs.
Astonished to find that while I am, sadly, neither the sluttiest nor the most pervy member of HF-Hentai, I seem to be the most experienced. Come to me if you need any advice! Well, if you're silly enough to trust OKcupid tests.