Yes, our underwater camera for snorkeling supports instant playback of videos directly on the device, and you can also upload videos to a PC for viewing. 

This is more a question of your glasses and not the lamp. She produces light. If your glasses have an anti-reflective coating, the lamp will not be reflected in the glasses, depending on the level of anti-reflective coating. (It should be noted here that the anti-reflective levels trigger different colors, level 2 triggers a blue tone in the glasses, level 3, which is the most recommended for working on the PC, triggers a green tone. This goes badly with a green screen , if the plan was to connect this to it) 

You can use the gimbal as a simple 3 axis stabilizer for your phone without using the app. So just use your normal phone app at whatever resolution you need. My V60 does 8k video. 

Our tripod is 1/4 size quick release plate, 3/8 size gimbal interface size, you can check with your blackmagic pocket cinema camera 4K screw that it will fit for it or not. 

Yes. The binoculars have adjustable rotating eyecups. Those who wear glasses will be more comfortable viewing with the shortened eyecups, while those who do not wear glasses usually prefer the longer eyecups.