The short version. Magyarize collects nothing. There is no account, no sign-in, no advertising and no analytics. Your photos never leave your device, because the app has no networking code at all and no server to send anything to.
When you pick a photo, iOS hands the app a copy of that one image. Everything after that happens on your device: finding the face, placing the stickers, and producing the finished picture. Nothing is uploaded, because the app cannot upload anything.
The app never asks for permission to read your photo library. Picking a photo goes through Apple's own picker, which runs outside the app, so Magyarize only ever receives the single image you chose and never has access to the rest.
When you save a finished picture, the app asks for permission to add photos, and only that. It cannot read what is already there.
The app uses Apple's Vision framework, on your device, to find where a face is so a sticker can be placed correctly. It measures position, size and angle. It does not identify anybody, does not create or store a face print, and does not compare your photo against anything. The measurements last as long as the picture is open on screen and are then gone.
A small amount of app state, such as your preferences, in the standard iOS user defaults on your own device. There is no personal information in it.
The app is rated 4+ and collects nothing from anybody, of any age.
If this policy ever changes, the date at the top changes with it.