Comment 5 for bug 1251832

Its normal and expected for a webapp used through Firefox to have both the Firefox window and the webapp window.

They'll be represented by one icon if you use chromium (it will have to be your default browser though).

Not being prompted for for desktop integration probably means the system still thinks you have the integrations installed. In the steps above, kill the 'unity-webapps-service' process before you move the files out of .local/share/unity-webapps/ and see if that makes a difference.