Hey there Andres!
Thanks for reaching out — that’s a great question, I can help with that 🙂
It sounds like using BuddyPress with The Events Calendar will achieve the features that you are looking for. On it’s own, TEC doesn’t provide that sort of social functionality but can be added with BuddyPress.
There may be a bit of customization depending on the scale of integration you are looking for. Basically TEC would handle the tasks relating to events and the third-party BuddyPress would hand the social aspect of profiles and messaging.
Hope that helps!