No, every flag is reviewed by a mod. Extensive, unneeded flagging is actually a reason to get in trouble.
There are always ways to contact moderators in person to point out that someone is singled out by a groups, so that the mod can keep an eye on it and step in if needed. There are really not many other steps that can be taken by a site to stop bullying behavior - our forum very often polices itself with members stepping up for others. You may think that doesn't happen, but it does.
Mods see exactly who flags - you're only anonymous to other users.
I believe there already is a limit. We reached it often when we were flooded by spam bots.
Case by case basis. Some messages are flagged because of personal reasons, and then the flag is usually removed.
Yes, the messages are all read.
Sometimes users remove their own messages, not sure if you mean that. If multiple people flag a post at the same time, it gets auto-hidden and mods restore it if we disagree with it.
Posts are sometimes closed when the conversations have run their course, or if a topic had been discussed in the past and turned ugly. We work with experience at times and don't wait for you guys to become mean to each other.
Also, when a thread receives many individual flags we often decide to close it. It very often means there is a major issue with the thread.
When a thread is long, we also simply don't have the time to read through a hole thread to clean it up and only hide the posts that are the potential issue. Closing it is the simplest solution, even if you don't like that solution much.