They are flickering very fast. Persistence of vision smooths this out so your brain perceives a steady light. With the camera it is capturing some frames with the lights on, others off, due to a frequency mismatch, so it looks like they flicker.

LEDs control brightness by blinking on and off really fast the and your camera's frame rate is out of sync with it. Same thing can happen pointing a camera at older TVs and monitors.

Sure. You also can ask David Icke. He explains why we can't see reptilian shape shifters. The human eye has a very small range of light seeing frequency. I think just about 0,05%. In fact we are blind.

Alturnating Current running through Light Emitting Diodes.

Diodes only allow current 1 way.

The power supply is switching directions 50 times per second.

This flickering is imperceptible to the human mind but is not good for your health. It's why people say LEDs aren't good for you.

Your camera is recording so many frames (eg 30) per second..