I think Karen should respond to the requests with something like, "Thank you for the interest, but it would be inappropriate and unprofessional of me to select students to participate in my wedding." Because it's true.
Those parents have some nerve.
This, or "It would be unfair to pick one student when I care about them all, so I will not be having any students in my wedding party because I don't want any hurt feelings."
When I was in the third grade (eight years old) my teacher was a close family friend. She had actually dated my oldest brother when they were in high school, before I was born. She got engaged during the summer before the school year started and was married the weekend that the Easter holidays began. My mother instructed me that I was not to ask about being a flower girl under any circumstances, and I didn't; but several of my female classmates did ask. She was very sweet to them and explained that it wouldn't be fair when there were so many little girls that she cared so much about.
A few weeks before the wedding my my teacher took my mother and me to lunch at the fanciest restaurant that I had ever seen in my eight years. She gave me a little heart shaped pendant necklace and told me that she wished she could have had me be her flower girl, but couldn't because the other kids might not understand. I did go to the wedding with my family and the bride made sure I had a special bit of cake to put under my pillow that night.
Even though we had a previous relationship
, I can see the argument that even this much extra attention could have been considered unprofessional of my teacher. I can't imagine how a parent could think it was appropriate to ask to be part of a teacher's personal life like that, or think that such a request/suggestion would be appreciated. If I were the OP's friend, I think I would be insulted that my student's parents think that I would even consider these "resumes".