Jack, I realize this sounds strange, but it's technically SORT OF possible. Explanation:
The way I immediately think of doing it is by use of an image, but this could not be a background image, so could not be a small box of a color that would then automatically repeat. You would have to create an image that would occupy the full width and full length of the space occupied by the profile - in other words, a VERY large image. You would then link to that image on the first line in the biography space, and use the wrap parameter in the image template, specifing: wrap=y
As to your second question, there are several reasons (all technical, not aesthetic) why I do not think that is a good idea.
While writing the above, I thought of another way to accomplish your goal, with less negative technical impact. If you create a table, you could then use color background for specific cells. In this case, you would create a table to start with, then put the entire page content in a single cell of it, making that cell whatever color you want.
EDITED: I realize this isn't what you're looking for, but just a suggestion you might want to consider because it would be extremely easy to implement. How about creating an image, perhaps with yellow background and repeats of a question mark logo, that you would use as a page background. This, of course, would only appear on left and right sides of the page in whatever excess screen width is available, so some users would not ever see it.