Most questions have an answer here. If yours does not, write to us — a person reads it.
Yes, all of it. The cutout runs on the device's own hardware, and nothing is uploaded. If you turn on Airplane Mode the app behaves exactly the same.
Open the photo and use Touch up. Restore paints the missing part back and Erase removes what should not be there; pinch with two fingers to zoom in for fine work. The corrected version is what gets exported.
Turn on "Glass or clear product" in the export screen. It clears the surface that shows through the product and lowers the amount for tinted glass. It works on a plain surface — a patterned tablecloth will still show through, so shoot glass on something plain.
No. Open Settings and tap Restore purchases while signed in to the same Apple Account. The unlock is permanent and is not a subscription.
Wherever you chose before the run — any folder the Files app can reach, including iCloud Drive or an external drive. The app writes them there and keeps nothing of its own.
That photo had nothing the cutout could separate from its background, usually because the product fills the frame edge to edge or is the same colour as the surface behind it. Reshoot it with a little space around the product, on a surface a different shade.
Questions, problems, or a photograph that came out wrong — send it and we will look at it.