How can I be sure that this iPhone app won't use my personal information?

Start by checking if the app can track you by going to:

Settings > Privacy & Security > Tracking If the app is listed and enabled, disable the app.

Then go back to the Settings main menu and scroll down to find the app. Apps are categorized alphabetically. Tap on InstPower in the list, there you can disable location access, access to photos, etc.

Once it's done, you can't do anything more.

If you are concerned that the app developer is not trustworthy, I'd consider uninstalling the app.

Buy your own external battery pack.