I have a question regarding the page with the search results.
Since I have a white H1, on the search results page against a white background the H1 is not visible.
Can I change the background-color of just this one page?

I would suspect so. Just look at the page source or perhaps use Firebug to determine the proper code.

I've tried with the 'firebug' of Chrome but couldn't find the background properties.
Is it so that the results page is kinda like build from a php script?
I've looked at the button 'search' to see what script it calls to, but that didn't gave me much clearity...

I can't say without seeing the site.

The site's in Dutch, but of course you're welcome to have a look:
http://www.marktmonitor.com/
In de right sidebar is the search field. If you type in 'innovatie' you'll get a nice page with search results.

You have all sorts of choices. You could change the title color on search results by using the following

.search-results h1 {
    color: #993399;
}

Or you could change the background color of the middle section by using this selector instead

.search-results #middle

May I ask why you have h1 set to white?