samsung galaxy note 2 android version 4.1.2
I know that this question was asked before and the reply was not possible
How to display balloon counter over application launcher icon on
Android ("vanilla" android without custom launchers and touch interfaces) does not allow changing of the application icon, because it is sealed in the
.apk tightly once the program is compiled. There is no way to change it to a 'drawable' programmatically using standard APIs. You may achieve your goal by using a widget instead of an icon. Widgets are customisable. Please read this :http://www.cnet.com/8301-19736_1-10278814-251.html and this http://developer.android.com/guide/topics/appwidgets/index.html.
Also look here: https://github.com/jgilfelt/android-viewbadger. It can help you.
As for badge numbers. As I said before - there is no standard way for doing this. But we all know that Android is an open operating system and we can do everything we want with it, so the only way to add a badge number - is either to use some 3-rd party apps or custom launchers, or front-end touch interfaces: Samsung TouchWiz or Sony Xperia's interface. Other answers use this capabilities and you can search for this on stackoverflow, e.g. here. But I will repeat one more time: there is no standard API for this and I want to say it is a bad practice. App's icon notification badge is an iOS pattern and it should not be used in Android apps anyway. In Andrioid there is a status bar notifications for these purposes:http://developer.android.com/guide/topics/ui/notifiers/notifications.html So, if Facebook or someone other use this - it is not a common pattern or trend we should consider. But if you insist anyway and don't want to use home screen widgets then look here, please:
As you see this is not an actual Facebook app it's TouchWiz. In vanilla android this can be achieved with Nova Launcher http://forums.androidcentral.com/android-applications/199709-how-guide-global-badge-notifications.html So if you will see icon badges somewhere, be sure it is either a 3-rd party launcher or touch interface (frontend wrapper). May be sometime Google will add this capability to the standard Android API.