When I am editing "Image" content type there is an option:
Where can I changes sizes of these previews? And regenerate the corresponding pictures?
These are the same settings as for your normal image styles. You can manage them here: admin/config/media/image-styles. Klick on edit on the rhs, then "override defaults", then edit the effect.
From your image it looks like you are setting the image style of the preview. This is the admin/editor preview of this image field (when editing content). If you would like to set an image style shown to the public, the easiest way would be to manage display for your content type and choose an image style for your image field there. (Look for the manage display tab)
As Volker said you can edit image styles and create new image styles here: admin/config/media/image-styles and then use these in your manage display settings.