1. Yes. I think it's an improvement.
While insulting someone is obviously wrong, it's not the mods' jobs to police it. Instead, I think it is the community's job to rebuke the offending members. Trolling really depends on the intention of the troll. I don't mind friendly ribbing or just messing with someone, but when someone has malicious intent, it is once again the community's job to rebuke the offending members. If they aren't listening to the rebuke, then ignore them. They revel in getting people riled up, so don't give them that power. If it becomes spam, then there is reason for the mods to step in.
Streamlining and codifying it is excellent, as any rules or laws should always be easy to understand.
I don't see much protection of children, but I do see an age requirement to make an account, which is definitely a good thing. I don't think Little Timmy should be on this site.
I'm a little concerned about the "no moderator harassment" rule because it all depends on what they define as harassment, but I'm going to give them the benefit of the doubt when they say they'll have thick skin. Mods, please do not betray this trust I have in you.
2. Yes2. Sharing PMs may be needed to establish what happened in say, a mafia game when someone C/P's their role and character to another player and the game host needs proof of the occurrence. However, private conversations should stay private in most cases. I am going to hope the mods understand that PM sharing must only happen when necessary, and that they must approve when it is necessary.
3. No. Expanding S&G would give it equal to or more power than the actual arguments being presented. Even casual debates must be argument-oriented.
4. Yes. A reason means that people can't just report a random post they don't like and hope the mods find a reason to remove it. They have to at least come up with their own reason on why it should be removed. In addition, it makes it very clear to the mods what they're dealing with.