Questions, bug reports and feature requests all land in the same inbox, read by the person who builds the app.
Email, with the macOS version and what you were doing when the problem appeared:
In the output folder you chose when running the production. Originals are never modified - ExhibitBench always writes new stamped copies.
The registry advances only when a production runs, so first check the production log to see the exact range that was used. Delete the stamped output if you don't need it, then create a new production - the registry keeps the record straight either way.
No. The app is sandboxed and has no network capability - no accounts, no analytics, no uploads. Your documents are read from and written to your local disk only.
PDF documents. Convert other formats to PDF first - the app deliberately stays out of file conversion so the stamped output is predictable.
Yes. A matter is a single file - copy it to the other Mac and open it there. The registry and production log travel inside it.