No, CB Blogs is only designed to function as profile blogs. Maybe consider just using stream posts? You can integrate CB Activity into GJ using the provided system actions in CB Auto Actions.

Is it possible at one point to make one stream post public and link to it ?

You can actually already link to an activity entry, but there's no feature to easily share those links yet. Such a feature is planned with the Share API that is not yet implemented. The below is the link structure if you want to try it. It will attempt to rebuild a stream to check permissions.

index.php?option=com_comprofiler&view=pluginclass&plugin=cbactivity&action=activity&id=ACTIVITY_ID_HERE

How can I use for instance tags with streams to make a private tag public then publish it ?

I don't understand what you mean by this. Tags in CB Activity are just tagging something with someone. It doesn't really do anything beyond that unless whatever you're adding those tags to decides to do something with those tags.

I thought at using activities, but it seems that the asset is only blog.xxx so what would you suggest to achieve it ?

No idea. Blogs and K2 articles have no clue a group exists. I don't see how you'd determine what group the create article and create blog pages even belong to.

Posting in stream is fine but only for small text, for longer blogs we would need CB Blog (configured with K2)

Long posts should work fine in streams. If they're too long for a standard mobile and desktop view (800px is the maximum tolerance) it will create a read more link to reduce it down to 400px.