1) Recently we change hoster and we do not receive notifications of undelivered e-mails in our Inbox.
Let me explain myself : guess that our website e-mail address is example@gmail.com. Previously, when we sent e-mails through the Community Builder users management system we got e-mails notifications of unsucesfull delivery in our example@gmail.com GMail address inbox when the recipient e-mail address was not correct anymore. Since we change hoster we do not get this e-mails notifications of unsuccesfull delivery and to be sure it was not because all our users e-mail addresses were correct we tried with an e-mail address we knew was not correct. Do we need to configure something to make it work again ?
Nothing to do with CB. That's all on your mail server. Review your mailer configuration in Joomla configuration and ensure it's correct or contact your host for clarification on their mail server usage.
2) Is it possible to view in the backend the sent messages ?
No.