Does the app show battery charge cycles and health information?

This information unfortunately is not accessible through the iOS API. In the past some apps managed to use the private API (which is explicitly prohibited by Apple) and sneak through the review process to the App Store or used various hacks to get this information such as the techniques described here:

None of these seems to work now.

Even if some apps in the future manage to find a new hack to display the battery info, this isn't the way I would go with my apps. I want to use officially supported API to be sure the apps keep working in the future and have no interest in risking my developer account by doing the prohibited stuff. (Despite this approach I had to remove some features in the past as Apple disallowed accessing certain APIs because of security.)