I saved my inkscape svg image to png format. It appears to be a transparent png image since there is no background. How do I make the background color white? I did not see anything in the document properties which would allow me to make the background color white. I also tried to make a rectangular shape and color it white, but when I set the color to white, it disappeared and I could no longer select/move it.

You can change background color of your document in Document properties, it's in the top right corner, click on it to get a popup where you can change it. The default is transparent so you have to move the A slider to make it opaque, then choose any color you like.

As for the rectangle example - it can also work, if you have trouble selecting it because it's "invisible" you can always pop into outline mode and you'll see it's outline there, and be able to select it.