I'm not sure where you meant for me to go to when you said go here in your other post. But I found a tutorial on creating a child theme and so I went ahead and did so as per the instructions. It seems like it works. I activate the child theme in admin and it looks just like the original, so I guess it is working.
Yes, the site navigation is in that header area on the right side at the top. There is another optional type nav menu just below the other but I removed it in the admin panel to make more room for the logo.
OK, so next I replaced the entire code in header.php with code from pastbin and now my entire logo can be seen, but the header space has not changed. I had accomplished this before when I was trying to figure out how to increase the height of the header but did not like the way it looked and changed it back.
This is not what I am trying to change, or at least, it's only part of it. Probably, I'm not explaining what I want to do correctly or I'm describing the wrong area on the page.
I want to increase the height (space) of the white strip that goes across the header area so that my logo will fit within that white space area and blend in with it. The way it is now still looks like the logo does not fit there so I will need to increase that white strip at the top of the page.
At the bottom of the page in the footer area the white strip is 2-3 times bigger than the top one. That is what I would like to be able to make it like at the top of the page.