A:AnswerNo. It seems that the bose have a smaller adapter @ 2.5mm. The receiver is a 3.5. I don't know if there might be an reducer adapter you might b able to find. Or there is another Bluetooth wireless adapter for the bose qc25 by AIRMOD that will work. Search AIRMOD.
A:AnswerYes, these can receive a Bluetooth audio signal, amplify it to suitably drive headphone speakers, and provide basic shuttle controls. It does have a mic for phone calls.
It sounds like what you want is a Bluetooth audio transmitter.