Yeah, usually on a Monday there will be a bunch of articles approved in the morning. It seems like it's when they have time to okay them.
Having links to parts isn't an issue. People do that all the time. You probably didn't do anything wrong, it just can take 2-3 days before it's approved.
I don't even know what is involved in "okaying" an article. I think they mostly just see if it's spam or not. You'd think they wouldn't allow swearing, but I've seen a few videos that were published in articles that had swearing. Then again, I'm sure they don't actually watch any of the videos. Just a quick skim of the content.
I don't know what the set amount of published articles are before you bypass the wait. All I know is that I personally bypassed it and when I click "Publish" it is instantly up on the site. I want to say it was like, 6-8 articles. I generally try to use this to my advantage and get articles up on the site when there aren't any other one's being published. Not so mine get more attention, but so it's a more steady flow of articles.