Yes, Moto Z2 Play does have OTG support.
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.
Moto Z2 Play has protection against water. It comes with water repellent nano-coating.
Yes, Moto Z2 Play does have the memory card slot.
Yes, it does support OTG.