Reduce the height of the Upper boarder (where the logo & site title renders) and the Page banner

Hi John,  so for the white space with the search box at the top there is no much you can do at the moment.  That being said, they announced at Ignite that they will be releasing 3 options to adjust the size of the header area. That was for modern sites, but I imagine that it may work for a modern page in a classic site.  

For the image banners you should be able to edit the web part and see an "X" option on the left. Clicking this will allow you to remove the image.  Alternatively, they are releasing the ability to choose 4 formats for the banner area.  One option allows you to remove the image just leaving the title. I currently have this option available in my developer tenant, but not yet in our production tenant.

If you are desperate you could create a SPFX extension that overrides the CSS and hides those elements . DISCLAIMER:  This is definitely not a best practice and a non-sanctioned customization practice.

Hope this helps,

Dave