yitz: I know with Wi-Fi Alliance Miracast screen mirroring many devices (i.e. the 'sending' laptop, tablet, phone etc.) will use the same channel they use to connect to the AP to transmit the mirrored picture to the receiver. If the channel was already poor quality as suggested above, it may not be able to handle the data throughput required for screen mirroring and this can have an impact, so in this way whatever channel the HG659 has picked to transmit on can have an impact on screen mirroring.
Airplay doesn't use WiFi-Direct. Airplay receiving device sets up an independent connection to the source (over existing infrastructure mode wireless or wired network).