To adjust the width of the menu on the right edit customer/home.tpl, you'll see the <TD> tag after the main content that you can simply insert a WIDTH= into to stretch it out more.
As for the cart information in the header... Edit customer/menu_cart.tpl and take some of the code from this and put it into the head.tpl, then comment out {* comment *} the customer/menu_cart.tpl in the customer/home.tpl and move the include for the newsletter in its place.
There are many tpl's but once you edit a few carts you will slowly learn where each part of the site is, you can also enable the debug console in the Admin -> general settings to see what files make up the page your viewing OR use the Webmaster mode.
hth.
