Hi Kathy!
Thanks for considering our Events Calendar plugins and I’ll do my best to answer your question. The Events Calendar is designed to be a single calendar and so supporting multiple calendars can be done however it will take some additional customization/work to get it to function as you outlined.
First to display 12 distinct calendars you would have to make use of Categories. By having a distinct Category per group you can provide distinct calendar views that would only show their events. You can see how this would function on our wpshindig.com website. A sample category view is : http://wpshindig.com/events/category/wordpress-meetups/
If you wanted to limit which calendar the user sees by the group they belong to you would have to write custom logic to restrict their view/access.
As for your second question you would need to get the Community Events add-on to allow users to submit their own events. You would also have to ensure they put the event to the correct category to have it show up on the correct calendar.
Does this answer your questions? If there is anything you want further details on please let me know.
– Matthew