If there are no answers to these, I’ll just make my own estimations or try to work material around the issues in a generic fashion. Fun! It’s actually been a while since I’ve watched the anime, and I no longer have the first 2/3 to reference. I’m aware of the drama CDs and some of the DVD specials, but I don’t have direct access to those either (some forums have translations of some drama/radio CDs, so I’ll try to go off those if I refer to any of that material). Mai-HiME-only universe.
(1) Just how old was Natsuki when she was orphaned?
(2) There was no mention of her father, but there was that image in the anime of a man walking away with a woman. Thoughts? Or just random.
(3) How does voting for class president/student council members work in Japanese schools? (Can positions be inherited or not?)
(4) I don’t remember exactly when Shizuru met Natsuki (how old they were/what classes). I think these are in the DVD specials or drama CDs…
(5) I’ll be referencing materials like Wikipedia and matching Talk sections, but the Japanese schooling/education system articles at Wikipedia are out of date. (Can’t tell in what way.) I know terminology differs a little depending on sources: elementary/grade/primary, junior high/middle, high school/senior high school/secondary* (secondary might be used to include both middle and high school). Recommended links to current Japanese schooling system (or even more information about Fuuka) would be nice.
(6) I’ll have to do more research in the collegiate system, but AFAIK there’s the entrance exams, and you cannot double major (true?). Rules on dorm/apartment living during first year, cafeterias, etc…
(7) Youko’s (don’t know how they’re spelling her name on the DVDs) clinic: She’s a full doctor and not a nurse, I’m assuming? I don’t know how clinics in Japanese schools work at all or just how much equipment is available (IV drips?). Eh. Maybe too much effort.