For the white background around posts, look for this in your css around line 2302 and remove or comment it out –
.home .entry {
box-shadow: none;
-moz-box-shadow: none;
-webkit-box-shadow: none;
background: none;
}
They have it designed that way for a reason (can’t remember why) but removing or commenting it out will fix it.
For the menu – Since you don’t have that many menu items, you can remove or comment out the code on line 3996 in your style.css and it will move back to the right side –
.content,
.site-header .widget-area {
width: 620px;
}
Removing that defined width should make the nav float to the right since it’s a small menu.