Good question.
You can change the background colour across the whole survey via the survey settings. This can be done via your CSS selected style or simply by changing the background colour setting.
On a question by question basis you can change the background colour by inserting some CSS code under the advanced headings as such (you may have to tweak some of this code?) ...
<style type="text/css">
body
{
background-color: #FFFF66;
}
.page_header
{
background-color: #FFFF66;
}
.page_footer
{
background-color: #FFFF66;
}
.question, .submit_div, .progress_bar, .page_error
{
background-color: #FFFF66;
}
</style>
You could also review this post -
https://www.sawtoothsoftware.com/forum/2652/depending-on-uid-load-different-css-stylesheet?show=2652#q2652. It shows how you can load a new CSS file part way through the survey based on a condition. Your condition would be something that indicates the last question of survey 1 has been answered.
Another suggestion is you set up survey 1+2 separately and link them at the terminate page of survey 1. Survey 1 uses CSS style 1 and survey 2 uses CSS style 2. The only differences in the 2 CSS style files is the background colour settings.