I wish I could make a video with the racks I made. Do I have to ask permission to someone? To the manufacturers of all these modules? Are these original pictures from the manufacturers copyrighted? Or is it free to use?

The module images on ModularGrid are uploaded by users, so their rights are not cleared by manufacturers.
Since it is a great and free way of advertising manufacturers typically do not complain. But dependent of the context of your video if you want to be sure it may be good to ask them.