1. Not sure what you mean by this question. If you're referring to that you can make threads despite not being a member of the group/not being able to see it because the group is private, that's a site glitch. It happens all the time in the Community Hangout group. It's somewhat annoying.
2. Am pretty sure members are members of the site, public means guests (as in those viewing a thread but are not members).
3. Open Groups are those that can be joined at one's leisure. Moderated are ones where people can request invites and the owner then allows them. Only private groups you need to directly ask for an invite such as the Leaks Group.
4. Not sure what you mean by this question either.
EDIT: @
aldelaro5
1: that is what I meant, thanks!
2: I tried to access the group section as guest, you can't, so, why there's a distinction if both do the same in the end?
3: ok, so, I can request that another user receives invite, but let's say I want to submit a request for myself, can this works for my own usename too?
In other words, can I request my own membership?
4: If you're the creator (or have got permission from him), you can set the group permissions. There's a box for warn a post and even tough I should have the permission (I even see the word "warn" on other's post), it says that I do not have the permission to perform this action. I also learned that if edits on a posts exists, you can use the history function if you're mod, but even tough I have that options on other's post, it does the same error.
So, why this options exists if I can't use it?
EDIT: btw, tags don't do alert on edits