Time Lapse video by Very Large Telescope

[zenmaster]

Any idea what the laser beam looking ray is at around 2:50 is?

It's a laser beam which provides a reference for adaptive optics to help remove atmospheric distortion:

"A laser beam is transmitted from the telescope into a layer of mesospheric sodium at 56–62 mi. (90–100 km) altitude. The laser beam is resonantly backscattered from the volume of excited sodium atoms and acts as a guide-star whose position and shape are well-defined except for the atmospheric distortion. The light from the guide-star is collected by the telescope and a wavefront sensor determines the distortion caused by the atmosphere. This information is then fed back to a deformable mirror, or an array of many small mirrors, which compensates for the distortion. As a result, stars located close to the guide-star come into a focus, which is many times better than can be achieved without compensation. Telescopes have operated at the theoretical resolution limit for infrared wavelengths and have shown an improvement in the visible region of more than 10 times. Atmospheric distortions are constantly changing, so the deformable mirror has to be updated every five milliseconds, which is easily achieved with modern computer technology."

Are those shooting stars we see periodically in the video?

Yes, and airplanes.