uno.edu/computer-science is not a subdomain, but a URL. A subdomain would be computer-science.uno.edu.
The DNS server of the top-level-domain edu will reference to the DNS server of your university (uno.edu) and that one manages all subdomains on an local DNS server (like the aforementioned computer-science.uno.edu for instance). However, it's also possible that your university does not host an own DNS server if they don't need to manage subdomains.
And yes, Windows Server can certainly handle remote requests.