The answers seem to be no.
Yes, you can run the application installed on the client also in the browser. However, not all installed application features will be available. Anything that requires increased trust will not work in the browser.
No, you cannot run an installed application programmatically from code running in a browser. The best thing you can do is to show a polite message to the user that he already has this application installed, and in order to gain access to all his functions, he will need to run it.
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