That story wouldn't happen today - B&B even stopped a story with Amber and underage Thomas because of the Janet Jackson nipple backlash.
There was some speculation, more like rumor, that the hypnosis story was some type of a pitch from Hunter Tylo, as, around these years, she had spoken about cult-like behaviors which badly affected her and her family (several different instances of this), and that this may have also been a view she or someone had of psychiatry. I also wonder if, beyond anything with Hunter Tylo, that some on the show may have had a negative view of psychiatry, given their religious beliefs. Either way, the story was dropped very quickly, and I think they either realized it was too hot to handle, or that it was just unworkable.
The show really wanted people to love Amber so Stephanie was a big part of that. Today Stephanie is mostly just a gorgon until it's time for a health crisis. Lazy.
The guy with the glasses was the assistant of Pierce (the psychiatrist/hypnotist). It was implied that he was in love with Pierce and would do anything, including hypnotize Taylor without Pierce knowing. He made some sexually suggestive comments to Ridge which raised some eyebrows at the time. Paul Williams got a lot of praise for his performance.