Your cards, classes, schedule and deadlines are stored on your device, and synced through your own iCloud account. There is no Reps server anywhere, so nothing you write is ever transmitted to BSR LABS.
That architecture is the reason for most of the answers below.
Nothing. No account, no sign-up, no login. No ads, no trackers, no analytics, no third-party SDKs. The App Store privacy label reads Data Not Collected, and it reads that way because there is nowhere for data to go.
You, on your own devices. Nobody at BSR LABS can see any of it, because none of it ever arrives there. That is a property of how the app is built rather than a policy anyone has to be trusted to follow.
Sync runs through the app's iCloud Documents container in your personal iCloud account, under your Apple Account and Apple's terms. Apple holds that file the way it holds your other iCloud documents.
No. There is no model, no data pipeline and no analytics, and there is nothing to train on because nothing leaves your devices.
Reps is fully functional with no connection, airplane mode included. Everything you do offline is saved locally and catches up next time you are online.
More answers on the help page, or write to [email protected].