Yes, Moto Z2 Play 64GB comes with latest 7.1 Android OS so you may not require to update it immediately but going forward, company will produce OTA updates.
Yes, it does support 4k Videos shooting as well playback.
Moto Z2 Play SAR value are as below:
SAR Value (Head): 1.455 WKg/1g
SAR Value (Body): 1.24 WKg/1g
Yes, Moto Z2 Play comes with the inbuilt battery.
Yes, Moto Z2 Play does come with free style mod.