Perhaps
this Site will help.
Regarding getting quick answers, you'll have to reckon with the fact that a lot of folk on here came 'temporarily' for their job and are single, haven't children in school as yet or send their children to an International School. Those who have settled down themselves may no longer have reason to log in every day.
If you don't have a lot of joy with answers, it might be worth searching on the Forum - things like 'Geneva schools', 'Geneva children' and see if you can find posts from folk who live here and send their offspring to school in Geneva. You could try PMing them if you cannot find the Info you need elsewhere.
Good luck with your search.