I was wondering if the Multi-language feature works for Community Builder ie if I set the language to another than default, will it switch over to the other language plugin?

Yes, CB loaded language is based off the language loaded by Joomla. So if you've a Joomla Spanish language plugin installed and a CB Spanish language plugin installed then switch Joomla to Spanish it will load Spanish for both.

And what about the fields? Do they have a second language possibility?

If your fields use language strings, sure. You can use language strings for field titles, descriptions, and many other parameters. You can then use language overrides to translate them in each CB language plugin you've installed as needed.

CB uses whatever language is loaded by Joomla as noted in my reply above. This assumes you don't have a language specified in your account overriding whatever Joomla has loaded.

CB will switch the language if you have a CB language plugin for the corresponding language. The only time it can override this is if you login and that account has a language set so it will always load that users preferred language.