As I already got one "Fanatic" gold badge. Is the "Fanatic" badge awarded multiple times at http://magento.stackexchange.com or any other community ?
No, you get the badge only once per site.
You can see this in the List of all badges with full descriptions:
gold; awarded once
However, you get it for the main site and the per-site meta separately. In other words, the per-site meta has its own "Enthusiast" and "Fanatic" badges.