Need helping editing header

I recently migrated from WordPress.com to my own domain (justanother24hours.com). I am using a Cutline theme in WordPress and I am pleased with the progress I have made. However, I want to edit h1 and the floating links as this is causing a lot of wasted space on the page. I want my image header to top the page and I want to hang on to all of the search data that sits in the header. You can see what I mean by looking at the site (the current image header needs some work but you get the idea). I am a total novice and would really appreciate some help.