Who actually reviews the edit? The actual creator of the post? Some Moderator? Who? Is there any reputation I need to reach, to be able to edit without requiring peer reviewing?
You need 2000 reputation to edit posts immediately. Anyone with the edit privilege can review a suggested edit, as can the author of the post (it's up to whoever acts first). Only users with 5000 reputation can see a list of pending suggested edits: before that, you can review those suggested edits you chance on.
For more information, see How do suggested edits work? on the main meta site.