Hey there Daniela,
You’ve got a great idea there for adding sharing buttons to events, but it isn’t something that’s currently part of the plugin. We have add-ons that allow importing from Facebook, but not the other way round. That’s actually a really good idea that I’d love you to add to your voice to our Feature Ideas page (https://tribe.uservoice.com/search?filter=merged) regarding that.
If you’re looking to modify the design of the page, our Themer’s Guide (https://theeventscalendar.com/support/documentation/events-calendar-themers-guide/) has some useful information for you. You might even be able to figure out how to add those social sharing buttons yourself! There’s more technical information over at Documentation (http://docs.tri.be/) which might be helpful too.
If there’s anything else I can help with, please let me know!
— Julie