Write to [email protected] — a real person reads it, usually answering within two business days.
The app version (Settings → the version line at the bottom), your phone model, and what you expected to happen. In Settings there is Send feedback, which attaches the app version, the platform and the in-app log to the message — it tells you exactly what is being sent before it goes, and it can attach a picture of the screen you were looking at if you switch that on.
The router is very likely on the breaker you just switched off, so the two phones lost each other for a minute. Nothing is lost: the siren is produced locally and keeps working, and the events are delivered as soon as the connection returns. Switch that breaker back on and carry on.
Solo mode works: the phone in the outlet calls out the breaker number aloud, you flip on its cue, and the app matches each power cut to the number it announced.
Settings has a siren test. Raise the phone's media volume, and place the phone with its speaker facing into the room rather than into the furniture.
Purchases are handled by the store, so a refund is requested there — and the two stores work differently, which is worth knowing before you write to anyone.
On Android: Google Play → Order history → Report a problem. If Play declines and you believe the app is at fault, write to us: a Play purchase is one we can refund ourselves, and we would rather do that than argue.
On iPhone and iPad: reportaproblem.apple.com. Apple issues every App Store refund and a developer has no way to return an App Store payment — we cannot refund you there, and it would be dishonest to promise it. Write to us anyway if the app is at fault: we will tell you exactly what to put in the request, and fix the defect.
What the app does with data is written out in full on the privacy page.