Every part of Reps works with no connection. Reviewing, writing cards, drawing, photos, the scheduler, the focus timer. Airplane mode included. Nothing is degraded and nothing is held back until you reconnect.
This is not a feature that was added. It is a consequence of how the app is built: your cards live on your device, and there is no server anywhere to check in with.
The places with the worst signal are often the places with twenty spare minutes in them. An app that needs a connection stops working exactly there.
Sync runs through your own iCloud account. Work offline for a week and everything catches up next time the device is online. Nothing queues up and fails, and nothing is lost.
If two devices were both offline and both edited, the newer edit wins and the devices converge. Editing genuinely different things on each device keeps both.
Downloading the app, and syncing between devices. Those are the only two.
There is no account at all. No sign-up, no login, no email address.
No. Everything is stored on the device. Sync catches up whenever the device is next online, whether that is an hour or a month later.
Yes, on that device. You lose syncing between devices, not the app.