See the rights you gave Facebook for using their services:
The difference between that of FaceApp and Facebook compared with Google is that Google compensates through the "Adsense" scheme but the truth remains that they and their workers have access to your data; they have access to even the device you use in accessing their sites and services, they use it for several reasons that will enable you have a better experience using their sites and services!
WHY THE ALARM ABOUT FACEAPP?
It is believed that the reason for the alarm on "FaceApp" is because it's developers are Russians! Is America scared of Russia? Why are they making it seem as if the rights "FaceApp" demand for using their services is fishy whereas it's a normal thing?
What is the worst thing that can be done with your information?
1. You might find your face on a commercial or bill board without your notice or being compensated!
2. For countries struggling with freedom of it's citizens for expression, their governments may demand details of anyone they want to track down from these sites and service providers or ban access to the app within that country if the app owners refuse to comply!
As for the issue of using your details for crime, please that is absurd because anyone can access pictures of anyone once they have been uploaded to the internet whether you use FaceApp or not. So, I don't think the creators of this app will go to the length of creating an app just to get information of people they will use for crime!
Right away, FaceApp has the right to any picture that has been uploaded to their app; if these pictures have already been uploaded and FaceApp already has them; you that your yard is yet to know your name, what is your fear?
Please sit back and enjoy technology!