It's just an apk... you should be able to sideload it with adb without root with adb sideload <your apk>
. It would just be removable since its not it /system/app, ie built in with the ROM. If the makers of your device disabled certain features on the device, which would explain possibly why those menus do not display in the Settings app, then TelephonyProvider may not be all that you need to get the connections you want to establish working.
Hope this helps.
Update: These features are probably disabled on the device you are using. based on what you described. From the PackageManager documentation.
FEATURE_TELEPHONY Feature for getSystemAvailableFeatures() and hasSystemFeature(String): The device has a telephony radio with data communication support.
FEATURE_WIFI Feature for getSystemAvailableFeatures() and hasSystemFeature(String): The device supports WiFi (802.11) networking.