Is it possible to have buttons in CB to share posts, blogs, groups in social networks such as facebook, twitter, etc?
You can share any URL on your site just using those platforms share buttons. You don't need any special implementation for that.
Facebook
Code:
https://developers.facebook.com/docs/plugins/share-button/
Twitter
Code:
https://developer.twitter.com/en/docs/twitter-for-websites/tweet-button/overview
Simply add them to a module and place them on any page you want shared. There's several extensions on JED that can help with rendering share buttons as well. There are no plans for embedding these and their external JS into specific parts of CB.
it is possible to have a free text search form in CB that searches users' activities, groups, blogs, events, etc. In summary a free text search form that searches everywhere in all CB?
You can already do this to an extent using Joomla's search module. CB Search Bot allows it to search CB users. CB GroupJive Search Bot allows searching groups. Blogs can be searched using normal Joomla content searching if its modal is set to Joomla otherwise no it can't be sitewide searched if using Internal. Activity cannot be searched as it's too heavy on the database and likely will never allow for it beyond possibly some sort of built in keyword filtering.