Only on your iPhone. There is no account and no cloud sync, so your history doesn't move to a new phone and isn't backed up anywhere else by the app.
Yes. Everything is on your device, so it works in the gym with no signal.
Go to Settings → Training Max and tap Reset training max on the lift you want to change. Workouts you've already completed or skipped keep their original numbers.
Go to Settings → Reset 5/3/1. This deletes your training maxes, settings, and all logged workouts, and can't be undone. Deleting the app does the same.
The app collects no data. Read the full privacy policy.