For Joomla articles to create activity entries you need to enable that system action within CB Auto Actions > System Actions. Note it uses CB Articles to integrate with Joomla content or K2 so CB Articles needs to be enabled for that activity entry to display properly.

If yes, how could I set plugins to allow comments in articles?

You can enable article comment streams within the CB Activity Bot within Extensions > Plugins.

Also, if yes, i suppose that every article will have it's own relative comments boxed under the article. Right?

Yes.

WhatI expect isacomment box and comments in articles where I want to show comments. Something like a classic blog articles with comments at the bottom of it.

That's exactly what enabling the comments in the CB Activity Bot will do.

Also I would expect that those comments can be displayed in CB Activity stream in user tab or module.

It will display the comments if there's an activity entry for that article. The comments will display as attached to the activity entry as would any comments on an activity entry (below it).

Now, those are my steps to try to follow your suggestion:
1) activated CB Auto Action plugin
2) inside system auto action I've activated CB Articles - Comment Notification
3) activated Content - CB Activity plugin

You need to edit the CB Activity Bot in Extensions > Plugins and enable commenting. There's a tab of parameters specifically for that functionality. In CB Auto Actions you need to enable "CB Articles - Create" system action if your want articles to create activity entries when the article is created. Next ensure CB Articles is published in CB > Plugin Management (should be by default). That's all that is necessary. "CB Articles - Comment Notification" is just a notification; it does not create activity.

Does the article activity exist in CB Activity > Activity? If it does it was created successfully and should display. If it's not displaying ensure that activity entry is published. If still not displaying ensure CB Articles is published in CB > Plugin Management as it's used for handling the parsing of the display.