Google will not show banner ads or other kinds of advertising on the search results pages. No, Google will show no banner ads or other kinds of paid advertising on the search results pages. However, Google may show a text link. The university name in the URL is done on a first come basis. If the name you desire is already taken, you will receive an error message saying that name is already taken.
Universities can search over one domain at a time.
At this point in time, you can not search over multiple domains at the same time. My site isn't launched yet. Google needs to have visited your site for your SiteSearch feature to work. Google only visits web pages that are linked to other sites on the web. Since the University SiteSearch program is subset of Google's web index, it needs to be accessible from public websites.