I am not good in .NET, but as much as I know it does not support .aspx files. I think you need Microsoft Visual Studio for that.
It fully supports asp.net, both 1.x and 2.0. You need to install the .NET Framework (downloadable from MS).
Visual Studio is not needed at all. Visual Studio is a (recommended) development tool which will speed up development. You can develop asp.net sites in notepad.
Of course you can run it. You only need the .NET Framework for that. Just download it and install it, and you'll serve up any asp.net page. You do not need Visual Studio to run .NET and/or ASP.NET. You certainly should not install Visual Studio on a production server.
Notepad can! I think you can make .net compile at run time but even if you can't all you need is the free .net SDK as I don't think the framework includes a compiler but could be wrong on this. Either way you can use notepad but personaly I'd use the free express edition of visual studio.
Yes it does. I remember once i have to setup it manually. You have to use aspnet_regiis utility to integrate the IE with your net framework. This is a cmd type routine which will run in the commandwindow. hope it helps