Ok - cant insert images into the editor!

Its here - https://drive.google.com/file/d/0B467FSv8x4UkNmlhN2xXZEZ6Zk0

There is a gadget that shows only Blocks (atleast in newer versions). Maybe it's sufficient to change to that one?

Which gadget is this and how do I change?

I see no way to ful remove the Assets gadget.

If you add a new gadget, there should be one called "Blocks". Not sure in which version it was added though. You are correct that you can't remove the Assets one though.. :(

Actually it is totally possible to modify the available components but only for users that have not modified their views, e.g. they have not added any components to their view. You can reset your view in the my settings page under the display options tab. The following code will remove the component, add this to the episerver.shell element in the web.config:

<viewManager>
  <views>
    <add name="/episerver/cms/home">
      <settings>
        <add name="RemoveMediaComponent" 
             transformationType="Remove"
             definitionName="EPiServer.Cms.Shell.UI.Components.MediaComponent"
             plugInArea="/episerver/cms/assets/defaultgroup" />
      </settings>
    </add>
  </views>
</viewManager>