It can definitely light up your campsite. It’s dimmable, I used mine to shine light on a park size bench for dinner. Lights up the entire interior of a tent. This can also charge your phone. 

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) 

All adjustable ND filters have this problem. The larger the focal length used, the less the cross shadow will be affected. There will be obvious cross shadows and vignetting in the large light reduction gear. If you continue to rotate, the shadows will disappear naturally. This is a physical phenomenon, not a product problem. 

Yes, it can run indefinitely after being plugged in. 

Of course you can, it is highly absorbent and you can stick it to any smooth place such as walls, mirrors, computers, iPads, desktops etc.