Admin - Configuration - Layout Settings - Categories-Tabs Menu ON/OFF to turn on the category listing in the header.
Admin - Tools - Layout Boxes Controller to turn oiff the Categories sidebox.
The width of your store is set in stylesheet.css in the #mainWrapper rule. You can set the width to either number of pixels (yours is the default 750px now) or percentage, up to 100%.
Before you make any more changes, create your custom override template:
http://www.zen-cart.com/content.php?180-how-do-i-create-a-new-custom-template
Also, if you're really using version 1.5.1, it would be smart to upgrade to the current (1.5.3) version before going any further.