Can I host a asp.net application on a linux based webserver?
Do they allow .net framework to be installed on linux?
Mono might work for you. It's an open source implementation of .NET that runs on Linux. It requires installation.
You can test your ASP.NET application with MOMA (Mono Migration Analyzer) first to see if it will work.
Check out the mono project: http://mono-project.com/Main_Page
It's not 1:1 to the .net framework, but it's as good as you're going to get on linux in terms of .net.
Although there is Mono project - an implementation of .NET framework for Linux OS, I'd suggest you to use Windows server to host your web applications, since Mono doesn't provide all .NET functionality.
Yes that is possible, if you have a VPS/VPC server.
In shared hosting server you coudl go for Windows/Plesk, as they have pre-installed ASP.net. In shared hosting Linux, you may not get root access to install ASP.net, please confirm over the specification from your hosting provider.
If you have a Linux server make sure that you " root access " to install the progamming language.