Hello Gayle,
1. Currently there is not a built in sharing links for events. We are interested in including that feature in a future release, but we don’t have a timeline right now. That being said, this could be possible using third party customization or perhaps via another plugin. You could check out these threads in the PRO forum where people are discussing options:
Integrate Social Media hype
Adding social media fields for Organizer & Venue
2. There is not a specific widget for categories (that I know of) but you can achieve the same results by making a custom menu of your categories and then using that in a custom menu widget. It achieves basically the same thing. If you’d like a more detailed walk-through of doing that just let me know.
Did that answer all your questions? Let me know if there’s anything else I can help you with.
Cheers,
Leah