Hey Mike, let me see if I can help you out:
1 & 2. You want to edit customer/main/welcome.tpl. That is the page that is displayed on the home page only. If you nuked some of the language variables, you can always find the original template in the skin1_original folder. You can use regular html in there as well, so go ahead and add logos to your heart's content
3. Are you talking about the headers of the menu boxes on the side? Do you want the same background for each or will they all be unique?