Hi Tony,
Both the free and PRO version of the Events Calendar allow you to specify categories for events. The ability to sort by category within the calendar view is not currently baked in to the plugin, although people have certainly done it with customization. One nice way of achieving a similar effect is to make a custom menu using the event categories and put that in your sidebar.
About an “add to my calendar” link- are you looking for a way that users can submit events to your site, or a way that events can be exported from your site to a user’s calendar? Or is it something else? I’ll be happy to help once I understand the question a little better 🙂
Thanks,
Leah