David, in response to your post:
1. Yes, you will need a web hosting provider that supports ASP.NET...which essentially means Windows-based hosting. Brinkster support Windows-hosting and also supports development on the .NET Framework (which includes ASP.NET).
2. Because Access is file-based, most web hosting providers support it. Brinkster for instance, gives you a databases folder which can contain Access databases amongst others.
3. It has nothing to do with the program or what features the program supports. How you connect to your database is up to you and usually written within the connection string. This can be done in code or visually within Expression Web.