The edges of the first and last child ARE touching the edge of the header. The nav and the header are the same size. If you’re talking about the text in the nav, you have 64px of padding on first and last child which are getting in the way of them touching the header edge.
Your second question I don’t quite understand. What area is the paper background not covering that you want covered? You set it to the background of whatever your containing tag is that all the elements you want with a paper background are inside. Your grid system to me a little confusing as you have all these class names like grid_12 and grid_3 but I don’t see much order to them without a lot of css cross-referencing. I take it you’re using them as guidelines to line things up? I’ve only use basic grids for layout design in photoshop so I may be misinterpreting their use here.
Also see you’re using HTML 5 markup. Just a heads up that some of your tags on the incomplete lower part of the page are being used incorrectly.