Okay, I am a regular on Trip Advisor, so I'll try and offer my 2cents worth. ( or go to the Trip Advisor Support Forum and hear pretty much what I've saying. ( and no I do NOT work for TA)
1. You can not respond to a Management Response. Each party gets their say. Trip Advisor will remove a review ( or a management response) if it is against guidelines. They do not fact check.
2. I believe they will allow the use of a first name, but I would contact them ( there is a flag next to the MR) and ask. If you insist and indicate that your name is NOT in your avatar they may take the MR down. If your first name is obviously in your avatar ie. from your screen name here, if you first name is Jim!
3. if you are so upset, you can take down your review and the MR will come down with it.
Hope that helps.