Hi dcasmr,
<blockquote>1.) Is there a way to use JA Social menu system to create Menus holders for each of the menu within a given category?</blockquote>
You need to go Menus >> Main Menu (default menu) >> Create new menu items (Category blog or K2 categories). Then choose an available category.
<blockquote>2.) Is there a product suitable to handling many menus and even putting them into modules?</blockquote>
By default, you can create a Menu module in Module Manager to show menu items.
I am actually confused about your requirement, Do you want your menu items to showup on specific quiz pages? It won’t look good / possible to show 100 menu items as default menu items for the whole site. Help me understand your idea and I will try to suggest you better ways of achieving that.
Leo