Is there a tutorial how to use it?
There's the following out of date tutorials, which will be updated when possible. Their info is still relevant however. There are also HybridAuth help pages that CB Connect provides a link to within configuration by clicking the link next to the Provider parameter under each social sites configuration.
www.joomlapolis.com/support/tutorials/99-plugins
Is there a way to have social community tabs like like a twitter for example, that show last twitter entries of the user for example or something like that?
CB Connect does not provide such features. It is strictly for handling the login and registration process. It used to provide some of what you're asking, but it became scope creep and caused more issues than helped. The best way to have what you're wanting is to use a Custom HTML field and use the embed code provided by Twitter. CB Connect stores their Twitter ID, which can be used in the embed codes. You can also store their Twitter Display Name, which is also used in some of the embeds by using field mapping.