Banner size

@mscserginho: It would have been better if you have posted your site URL as well. I see that you are using Catch Everest Free Theme. Then just go to “Appearance = Header” and upload the image size of width 1140px after you upload it use the button “Skip Cropping, Publish Image as Is” to upload the original image. Then you can add the following CSS in “Appearance => Theme Options => Custom CSS” box to remove the padding.
#hgroup-wrap, #hgroup { padding: 0; }

But you cannot keep the social icon and search in the header right sidebar. It will go down or you can disable that from “Appearance => Theme Options => Header Right Sidebar”

@mscserginho: The replace your css with
#hgroup-wrap, #hgroup, #site-logo { padding: 0; }

I don’t get it why the image has 300px. Can upload/select the image from “Appearance => Header” and select the crop area cover full image and click on crop and publish. Maybe this will help.