Antenna needs good matching to provide good performance. If you just connect a long wire to the antenna point, matching will be very poor but it still can receive and transmit. To achieve a reasonable reception, just 28~30mm length wire soldered to the antenna point will be ok.
On 13th Floor, the K4558 is an operational amplifier. The function of it is to convert differential audio signals to single-end audio signal. It is because all Bluetooth modules have differential audio out.