Mine usually take between 2 and three days to show up. I think it makes a difference if Laurel and Manu are busy and how many stories have been submitted in the last couple of days. More stories submitted the longer it takes.
Yes, they have to review all submissions before they show up on the site. I've only submitted one story, but with that one, there was about a week's time between the submission and approval of the story. I'm working on another one though... hopefully I'll get it finished soon
I had one rejected for underage sex because I used a high school student but never gave an age. As soon as I put in the story that the character was 18 it passed.