Regarding the Browser not launching your app, it works for me if I use an HTML <a/> tag on my webpage.
Are you invoking your URL via JavaScript instead?
I ask because I know there is this “quirk” with Android’s WebView Java class where it’s WebViewClient.shouldOverrideUrlLoading() does not get called for URLs invoked via JavaScript… and that’s the method that most native Android developers use to override URL handling.