How can I have an internet social live in these conditions?

[Shizaroo]

The world maybe cruel and savage according to your mother's perception but the world is a much better place because of these social networks. Tell your mother that all these sites have strict regulations, rules, security passwords and certain restrictions. Persuade or ask your mother to set up an account with any of them and she can, if she chooses to, monitor your online activity.
Pinterest is safe and reliable.

The banks have money in their vaults. Sometimes banks get robbed. Does that mean your mother doesn't have a bank account?

I have located some friends and relatives whom I have not seen for over two decades using FB.