They remain only in PrivatePDF's protected app container on your device. The app does not upload them.
Open a PDF in Library, tap Share, and choose AirDrop, Files, Mail, Messages, WhatsApp, or another compatible app.
Swipe left on it in Library or open it and choose Delete. This permanently removes the local file.
Scanning requires a physical device with a camera. Check Settings > Privacy & Security > Camera > PrivatePDF and allow access.
Yes. Creation, storage, organization, and preview need no internet. A destination app may require internet when you choose to share.