I do have certain queries while deploying a .net windows application
whether we need .Net framework to be installed in the deploying machine?
Yes. If it is not installed, then the setup wizard or your program can install it, or, alternatively, you can prompt the user to install it.
If not so, whether my application setup(.exe) includes compiler or class libraries integrated with the setup
The .NET framework is required, whether you include your class libraries with your setup.
As, well as can i deploy my .net application in any other platform other than windows, will it support the setup(.exe) format.
You can deploy your application to Linux and Mac with minimal modification using Mono. You can also deploy your .NET application to mobile platforms with your current code base, though this will require more modifications.