How do I access the existing running windows forms application through url?

I have a windows forms application and which provides a way to search the database based on the provided value. Sometime I need to open the application through a simple html hyperlink with the search result while loading itself. There are two questions/doubts from here.

How to access the existing running windows forms application as url? If this is possible, how can I pass the argument?
If the application is not running, we have to start the application and search the value. This also has to be happened when I click the link.

Simply we can say like, if you open a website link from your outlook email, the link will be opening in existing opened default browser or it will start the new browser(if the browser is not already opened.) I want to achieve the same behavior.
Seems to be the below post is somewhat related to my queries, but this does not solve my problem.
Activate existing browser window with given URL from C# application (without triggering reload)

You can't do this.  The default browser launches when you click on a link because it is set up in the registry as the default handler for hyperlinks.