For simple pages, it's safest to wrap your greasemonkey scripts in at least an unload handler: According to the "Authoring" page at http://greasemonkey.mozdev.org/authoring.html,
User scripts are executed after the DOM is fully loaded, but before
onload occurs. This means that your scripts can begin immediately and
don't need to wait for onload. However, replacing large parts of the
DOM (e.g. using innerHTML or outerHTML) at this early stage of
rendering is known to cause Firefox some trouble. In this case, you'll
have more success if you call your code in response to the load event
instead:
window.addEventListener("load", function(e) {
document.innerHTML = "Hello, world!";
}, false);
However, if the "main site" is constructing itself via a secondary ajax call to news.html, that won't be enough, because the data you want to manipulate won't be in the DOM yet when your script runs on the main site. You'll need to delay your script's execution until after the main site has finished doing its thing, so that when you try to do your thing there'll be the thing there for you to do your thing to. So to speak.
Have your script observe the DOM and wait to run until after news.html has been injected into the main site, or be lazy and start it after a sufficiently-long setTimeout.
(A clarification based on discussion in comments: Greasemonkey will only act on the site that was actually loaded in the browser; it will not act directly on every XHR request that site makes, even if that url was @included in the script. So if site "foo.com" ajax-injects content from "bar.com/news.html", and the browser loaded "foo.com", greasemonkey will not directly modify the "bar.com/news.html" request foo.com made; it can only work with the DOM that foo.com constructs based on what it got from news.html.)
