Re: Problem with 100% width- divs and in Firefox;
You're saving as a PNG24, but you're not utilizing it. PNG24 should be reserved for images using alpha transparency. Either remove the background on the image or save it as PNG8, JPG, GIF... scroll through your options in Photoshop and see which one is the smallest size while still retaining that visual quality you're after.
For the nav issue...
I would set your header.png image as a background-image in CSS, aligned right. Then float the nav li elements right with a margin-right on the container ul that pushes it off that right side enough to clear the tree.
Does that make sense? I'll give an exmaple in code if not.