TwentyTwelve Child Theme: A few design changes

I’ve made a child theme of the Twenty Twelve theme, and there are a few things in the design that I would like to change:

1) On the “Full-width page template, no sidebar”-page template, there is an area on the page which is above the footer and below the main text area on the top part of the page. This area is separated from the top part with two lines and to the footer with one line. No content goes in there, and I would therefore like to get rid of it from the pages. How can this be achieved?

2) Is there a way to adjust the distance between the title on a page and the menu at the top of the page? There seems to be a fixed distance which for my needs is too big.

Thanks in advance for your reply.