Depends on the area. In many areas trespass is a crime that qualifies for citizens arrest and a security officer can do just that and deliver them to the police. They are mostly talking about the practice of bring the person to a security office and identifying them for the purpose of issuing the trespass warning.

That is illegal if the person doesn't agree to it. Many security officers will either use CCTV or simply snap a photo with their cellphone to keep track of the people who refuse.

Also in many places as soon as the trespass notice is given, if the person doesn't move to exit the property in the most direct, safest way possible, they are now trespassing and can be arrested on the spot for doing so.

If a security officer tells you that you need to leave, and that you're trespassing and you do anything other than say "Okay" and move to the closest exit, you've violated the law in most places and if you're being a real dick, they can perform a citizen's arrest and have the cops come get you.

They mention that you can't put up their photo on a bulletin board, but I don't know about that. I think most courts would find that there is a direct interest for security staff to share information with each other, and if a person has been banned from the property they need to communicate that to other staff. Maybe a public bulletin board might not be okay, but I know some places that use binders or things like that