You can listen to FM radio with gqrx relatively easily, if you can navigate through hundreds of input boxes.
sudo apt-get install gqrx
Anything more complicated will require some coding knowledge, unless someone already created a library for that specific thing.
There is also a ready-made package to listen to GPS signal, unfortunately it needs an external amplifier and a proper antenna, because RTL-SDR is not sensitive enough for GPS.
Nope. The LGPL license only requires that the user must be able to replace LGPL libraries with their own version. In theory root access is not required, but it will require some heavy effort from the manufacturer to provide a way to replace system libraries without somehow leaving a huge root exploit. Unless they implement virtualization.