First, other teachers or staff members should help the teacher to a quiet and clean place, like the school infirmary if there is one. This allows the teacher to rest and recover.
It's hard to say if it's extremely popular in a general sense. Among certain subsets of 'Family Guy' fans who are interested in exploring different interpretations of the characters, it might have some popularity. But compared to more mainstream 'Family Guy' - related content, it's likely a niche area.
I'm not sure specifically which 'woman throws table story' you are referring to. There could be many such incidents where a woman throws a table perhaps out of anger, frustration, or in a moment of extreme emotion. Maybe she was having an argument in a restaurant and lost her temper, or there could be some personal issue at home that led to such an outburst.
It depends on the day. Sometimes Stewie might be in a bad mood and not be as receptive, but on most days, he likely enjoys the special time with Peter and the stories he tells.