It is for entertainment. It measures things like symmetry, proportion and face shape, which are not the same as attractiveness - what face analysis actually measures is deliberately blunt about this.
Nowhere. Analysis is 100% on-device across iPhone, iPad, Mac and Vision Pro, and no facial data is stored or shared.
Yes - live camera or photo library, with history so you can compare over time and share-ready result cards.
You’re browsing inside Instagram, and its built-in browser isn’t allowed to hand links over to the App Store. Open this page in Safari and the link will work.
Tap the three-dot menu at the top right, then choose Open in external browser.