Email: hoursleft.help+balanceleft@gmail.com
No. It stays on your iPhone. There is no account and the app works offline.
Settings > Export backup. Save the file, then on the new iPhone use Settings > Restore from backup. Attached files are inside the backup.
Open the account, tap "Payment report (PDF)", check the preview, then "Send or print report".
Check that the account has a plan, and that notifications are allowed for Balance Left in the iPhone's Settings.
No. Balance Left is a notebook. For free advice see StepChange, National Debtline, Citizens Advice or MoneyHelper.