I want to know why I can't watch a single video lesson even if I'm a premium member? It's only demos. I tought that it would be possible to watch a full video lesson a day. So, what happens with it?

Full video lessons on a daily basis are a diamond privilege. You'll need to spring for the increased privileges with a few extra bucks. Worth it, in my estimation ... though I haven't yet taken the plunge myself.

Yes, it surely worth it, also with chess mentor, but I would like some minimal privilege with my premium membership. I mean, I can play in many tournaments at a time but i would like some more! Anyway, chess.com is a great site. Also, why advertising video lessons on my online page: "try a video lesson" if I can't! It's torture!

maybe the staff member is trying to torture you into buying a diamond membership?

on this page: http://www.chess.com/videos

you will find 5 full-length videos on the right-side that you can view at any time.