X Windowing Free Open Source Software at Windows Desktop

I am using a ssh session for my org Linux box to do all my installation work. Recently I installed a X Serve app but could not start its execution cause neither I am sure if X Server is running or not nor of how the app output (X windowing app) would be rendered on a Windows desktop from where I am doing a ssh.

So how do we know that X Server is running on a Linux box via a ssh session and which Free Open Source Software I can use to render the app output (running on Linux box) at Window Desktop?