Header Editing Help

I am trying to make a few changes to my website header without having to use a child theme. The website is finerpartydetails.com Its a work in progress

1. I would first like to minimize the gap between the menu bar on the right and the text below it. I cant figure out where that gap space is coming from within the editor.

2. I would somehow like to incorporate the company logo into the front page, either as a background image or within the header. When I add it to the header the title shifts and then the menu bar on the right slides down. I cant figure out how to add the logo as a background image effectively.

Any help would be greatly appreciated.