Is there a solution which could keep information about actions and updating of data on the site? For example, there is a site. And it's necessary to create a news feed on the site. Approximately, like on the Facebook.

Thas is, if someone added a new forum topic, article or page of another content type, this event should be added to the news feed. Also if someone changed any page, information about it also should be added to the news feed. Also, if someone commented or liked something. Also if a new used added to the site. And so on.

I need to clarify, is there a solution, which could perform it ? And this solution should have opportunity to customize, which data should be added to the news feed and which data shouldn't. And I need to have possibility to customize its output design.

I don't want to try to use the dblog module for it. Moreover, the data on the dblog module can be deleted.

P.S. In my opinion, it's not possible to perform it using the views module only. Because views doesn't allow to use different types of entity, such as nodes, comments, users and so on in the same view. Therefore, I see the way to put it together using some entity, which keeps information about actions and which can be outputed using views.
By using the Message module (which already has a beta version for D8), you can create your own custom "Events logging" (to register things that happened in a site).

A great sample of this you can find in (the D7 version of) Commerce Kickstart, which uses the Commerce Message module, to create such "Events logging". In this case in the format of an Order History, as shown in this screenprint (from this module's project page).

The Message module is an amazing module, though there is not a lot of documentation about it. It is fully entity based, which implies that it perfectly (out of the box) integrates with modules such as Views and (only for D7 for now, not yet for D8) Rules.

Additional info

For more details about the Message module, refer to some interesting Use Cases detailed within its Community Documentation. And/or checkout the video introduction "Your Drupal site can talk" (if you want you can fast forward to about 03:30 where it really starts).