the TX/RX built in antenna of the mobile phone is designed to operate at the frequency range of the mobile radio standards of the air interface(GSM/UMTS).
So,to recieve commercial FM broadcasting,the head set it self will serve as dipole antenna at the range of ~100MHZ.
Yes. Cellphones have separate antenna for FM Radio. This is because FM radio needs a receiver of a frequecy band of ~ 90-120 MHz. That is why separate antenna is required.
You have to attach headset to a mobile to make FM work. Actually, when attached FM headset does a short circuit in the mobile and completes an electrical path which is necessary to make it work. When you remove the headset the circuit becomes open and doesn't work.
to achieve a good antenna gain at low requencies, you need to use a longer antenna because antenna gain is inversely relarted to "lambda", so they use the headphones themselves as this "long" antenna
Yes, cellphones have separate anttenna for fm radio. Have you noticed that there are some cellphones need to attach the headphones first before accessing to the FM radio applications? In that case, the headphones are reliable of connecting your signal from cellphone to FM station. Cellphones and FM radio have different paths so they need separate antennas to connect from their band.