What you're asking for falls under the category of site moderation, because it deals with modifying/removing content of other users.
Aside from being able to edit other user's content at the 2,000 reputation level, everything else you've asked for is diamond-mod-only functionality (and for good reason). Even at 10k, we have to vote to delete questions from the system, so we can't remove things unilaterally.
Content can be deleted automatically through flagging, but that's more for removing offensive/spammy material. If answers aren't useful for the question, then the voting system pushes the unhelpful answers to the bottom, and if the answers are paying enough attention, they will either fix their own content, or remove the answers themselves.
That being said, there are some situations where it's nice to keep the comments to a minimum. But at the same time, it's pretty rare that a conversation gets out of hand, or goes on a ridiculous tangent. If there's a problem or an exceptional circumstance, flag the nearest object for moderator attention, and they will decide how to deal with the situation. That's their function on the sites!