Currently I debug my C# application locally and use watch, breakpoint and commands like step into and the debug inspector.
setup remote debugging with another machine as described here: http://msdn.microsoft.com/en-us/library/bt727f1t.aspx
Is it possible to see the source code of remote application and go through it step-by-step as one can do locally?
Yes. Attaching to a remote process is just the same as attaching to a local process.