I remember when MS was developing Cassini - I believe they rolled it into VS 05/08, so I think this is a Cassini web server question.
I am using Windows XP with Vi
Microsoft doesn't allow this on purpose - they don't want you deploying your application with Cassini. It's compiled right into its code.
That being said, I've often wondered if they just check the url for "localhost". Perhaps editing the HOSTS file of the remote machine and redirecting "localhost" to the cassini machine could trick it? Worth a shot... In windows you can find HOSTS here:
C:\Windows\system32\drivers\etc
You can go into your web project settings and have it use the local IIS as a host instead, and then it will work fine.
You can use a Port Forwarding Utility to listen in on a port, say 5000, and then relay all that traffic to Visual Studio's port.
The solution is described in the article, Accessing the Visual Studio ASP.NET Development Server from iPhone.
I have written a blog post based on the above article which summarizes it, Accessing Visual Studio Web Server remotely.
To solve your problem of broken links, paths to files, etc. Use relative links.
Also, the token "~/" (without quotes) within URLs/path properties/values in ASP.NET's Server Controls will be automagically replaced with the real path to the IIS's subfolder where your application resides.
For this solution to work the root of the Web application you are developing must be an IIS Application (see your web project's properties pages at the Web section where you can find a link or button to create the IIS Application).
Google for IIS Web Application Root.