Yes, it's compatible with the Quest 3, according to their website: https://www.meta.com/ch/en/quest/accessories/link-cable/#tech-specs .
And yes, it charges the headset while it's connected to the computer.
No, you cannot connect the Meta Quest 3 to a Blu-ray player to watch the Blu-ray directly through the VR headset. The only way to watch movies is to watch them via the web browser or transfer them from a computer to the headset
In principle, you can use any USB-C cable. However, you may experience jerkiness in the game because the data transfer rate of most cheap USB-C cables is not sufficient.