I have a graphic that a friend made me in illustrator, and I need to resize it and change the background color. Though I've figured out gimp on my own, inkscape is totally new territory and I am so confused how to even access a simple color palate, let alone change the background color or resize. How do I do that?

Inkscape is a vector editor so you deal with objects, not layers. Select an object and you'll see some info in the status bar. If it's grouped you'll want to ungroup it or enter the group by double clicking so you can select individual objects. When an object is selected you can change it's color by clicking on the palette chips at the bottom of the screen or open the Fill and stroke dialogue for more control over color.

To resize the drawing simply select everything and use the arrow handles. Hold Ctrl to keep ratio and make sure the button for scaling stroke and other options are enabled on the Selector toolbar.