Anyone with the editor, moderator or admin title can access the admin section and therefore approve posts. So in short, anyone who is capable of hiding posts can also approve posts. There are no bots, it's entirely a manual process.
The discrepancy in how long it takes would be explained by our timezone coverage. Everything should be approved reasonably quickly when I'm awake, since I check periodically. However, I am by far the most active person doing approving stuff, so there'll be more of a delay over much of American waking hours. (Though the other mods are doing more than it seems.)
The process is reasonably simple. If you don't meet the point requirement in a given section, your posts are sent to the approval queue before they are shown to the public. We literally just press a button to approve each one, and they are made public instantly.
