Yes, Moto Z2 Play does have OTG support.
Yes, Moto Z2 Play comes with latest Android 7.1 Nougat OS and does support Screen Cast.
No. Moto Z2 Play does not have HDMI port but you can use HDMI connector.
Both colors looks very nice on Moto Z2 Play.
Yes, it does support 4k Videos shooting as well playback.