WP -- there is nothing wrong with walking, trotting and cantering a horse on pavement, though I don't know that I would canter very much especially with shoes on because it can be slippery.
What's wrong with bareback? He may not be the best rider in the world, but it's an ok clip, IMO.
No helmet? Ya, ok - for a rescue they should encourage safety at all times for public relations and liability reasons. Many people ride without a helmet. Myself included.
Walka -- I'm sure I've heard the same thing about shoes on pavement and it makes sense. The hoof will give somewhat, whereas the steel will not. No movement in the hoof = all the impact goes to the leg.