What permissions does the app use and why?
The app requires the following Internet/wifi/network-related permissions for the various tools it provides and the network information it shows:
INTERNETACCESS_NETWORK_STATECHANGE_NETWORK_STATEACCESS_WIFI_STATECHANGE_WIFI_STATECHANGE_WIFI_MULTICAST_STATE
Next, the app needs to access the device's location to show it on the map in visual traceroute and to find the nearest servers for the speed test (both available in the paid version only). Finally, the location permission is also required for the Wifi Signal tool — see this article for more information (Network Analyzer doesn't use the location information at all in this case). The permission used is
ACCESS_COARSE_LOCATION
which is the less precise of the location permissions, not requiring GPS and relying only on wifi and cell tower geolocation.
On Android 6 and later, the location permission can be disabled; however, in that case the above functionality won't be available.