I cannot see the vertices when they are selected why is that?
Is it a part in the video you don't understand (in that case include a time stamp) or is it something you are facing while attempting the course?
From the little to go off of, I'm guessing you don't see verts because you/or the video is in edge select or face select mode.
This was recorded with an old version of Blender 2.80, when x-ray vision wasn't that well developed. Nowadays it's easier to see selected vertices inside another mesh (but you'll have to enable X-ray Mode now).
I do not know what you mean, sorry.
There is a highly visible 'manipulator', that shows where the selected vertex is:
It's in the middle of the white circle.