Two-way communication between web application and desktop application

I am curious if this scenario is even possible:

1. .Net Windows Forms application (our product) with a couple of WCF services exposed (self hosted, for example on 'http://localhost:8000/myservice/method1'), running in elevated mode.
2. A web application (from another manufacturer) on a public domain, which would communicate with our application in a two-way mode:
   1. web application to desktop application: during the setup of our application we register a custom protocol 'xxx' (similar to 'mailto') and set our application as a handler for this protocol. So the web application can trigger an action in our desktop application with links in the form 'href="xxx:parameters"'.
   2. desktop application to web application: the web application would periodically (every second for example) poll our localhost WCF services via javascript ajax calls.

Is the 2.2 option even possible? Which binding should we use for WCF services? Are there any problems with cross domain calls (from public domain to localhost)?