I have been told to not have the pillow under my shoulders because then the neck does not have any support? Instead I was instructed to place the pillow just under my neck, to support the neck (with no gap under it). Please give me your opinion because this is not what I saw in this video.
What you describe is conventional wisdom but pushes the head and neck forward relative to the body. We want the head neck and body to approach being on a line. That's why we teach this configuration.
If the head protrudes forward quite a bit, add a second pillow below under the first, staggered, so the head has an additonal pillow's thickness under it and doesn't end up dangling backwards.