Headlines does not collect any of your personal data, period. Everything that you enter into the app, including favorite feeds and settings, is safely stored locally and synced between your devices using iCloud. Headlines does not display any advertisements, use any trackers or analytics.
If you so choose, Headlines can access your location to provide you with weather forecast. By default, Headlines will ask for your approximate location rather than precise coordinates. Your location is then passed anonymously to OpenWeather’s Weather API.
Headlines offers optional article translation capabilities. Such capabilities are provided by Google’s Translation API. Please have a look at their Data usage FAQ for more information (tl;dr it’s safe and private).