Moto Bluetooth headset with Nokia 5300: not a match?

I have problem using a Moto Bluetooth headset (received as a bonus gift back when I brought Moto E398) with Nokia 5300. First the pairing was not going smooth. and it failed a few times even after I entered the correct passkey "0000". Then even after I paired, I didn't seem to be able to get it working.

In addition, that Moto headset cannot be used to listen to music through Bluetooth. I
guess it only works with special bluetooth stereo headphone.

Overall, what a disappointment.