I'm not sure what's causing the problem with the tabs, but the background stopping partway down can be fixed by copying the background* selectors (background-color, background-image, etc.) from the body {} element in style.css to the body.pagebody {} element in style-artisteer-overrides.css. This is covered in step 7 on the Creating Skins from Artisteer HTML Templates document.
Unfortunately, the Artisteer skinning still isn't an exact science. We highly recommend that you install the Firebug Firefox/Chrome extension to enable you to inspect individual elements to determine where the style is coming from (or not coming from, as the case may be). Also, be sure to set the following keys in your user.config file while you're working on skins, and set them all back to true once you are in production.
<add key="CombineCSS" value="false" />
<add key="MinifyCSS" value="false" />
<add key="CacheCssOnServer" value="false"/>
<add key="CacheCssInBrowser" value="false"/>
Finally, keep in mind that if you are using Artisteer 3, the skinning document has not yet been revised for that version, as it's not completely finalized yet. Hope that helps.
Jamie