Is there a way to add "special effects", or "background photos" or "sticker" to the system so that the Facebook app can use?
What you're looking for is the Facebook Camera Effects



Example:

I added my simple draw, and I can see it on different designs, and also test it on my mobile before publishing (if you choose Preview on Mobile you'll get a notification in the Android Facebook app to test it).



Result:

I took a picture with my new overlay.