1. In CB, I'v added some custom CB fields for the registration. How can I get these labels translated, so that they show up in the right language when the user is switching between languages.
You'll need to add translation strings for them. For example instead of title being "My Field" it would be "_CUSTOM_MYFIELD". Then within the language files you'd define this string (don't define in cbteamplugins) as follows.
define( '_CUSTOM_MYFIELD', 'My Field' );
Using the above would allow multi-lingual support for field titles.
2. In CBSUB the same question. The descriptions of the subscription plans should change from language when another language is chosen by the user. (Same for the notifications emails)
You would use the same method as above or you could use the cbsubs language file and defined strings as follows.
'My Description' => 'My New Description',