Hey Tom!
We unfortunately can’t help with customizations or style/design tweaks here on the forums, but I can happily at least point you in the right direction for learning about how to make these changes on your site.
For adding a background image, this will require writing custom CSS on your site – you can write custom CSS at the bottom of your theme’s style.css file, for example.
Check out this article online for a great overview of adding background images with CSS → http://www.smashingmagazine.com/2009/09/backgrounds-in-css-everything-you-need-to-know/
As for the Google Icon, I did not see a Google Icon on your site – if you are able to find the icon, then your best bet is to use a tool like Firebug if you use FireFox, or the Developer Tools for either Safari or Chrome to find the CSS classname of the icon. Then, just like above, you can write custom CSS on your site to adjust its size and such.
Best of luck with your customizations!
— George