That should never happen — it is the one thing Loadwise is built to get right. If you see a machine or cable exercise after choosing "Dumbbells only", email us with a screenshot and we will fix it.
No. Loadwise has no account and no cloud sync, so your history lives only on the device you logged it on.
Settings → Restore Purchases. Use the same Apple Account you bought with.
Check iOS Settings → Notifications → Loadwise and make sure notifications are allowed.
Refunds are handled by Apple at reportaproblem.apple.com.