Yes, You will get Moto Style mod free in the box.
Yes, Moto Z2 Play does support fast charging. It takes just 30 minutes to charge 50% battery. You can get about 8 hours of use by charging for just 15 minutes.
Yes, it does support OTG.
Yes, Moto Z2 Play does support VR glasses.
Yes, but you have to buy a special mod for it.