IANAL, and if you want real answers, you just have to find one and pay him money. I literally know nothing, and this is all heresay:

So SP and FG are able to get away with what they do because satire is a form of protected speech, and artists are protected from copyright issues under fair use. But libel and slander are still a concern.

If I remember right, in the SP episode where Tom Cruise is in the closet (obviously implying that he is gay), the lawyers of the show were concerned with potential slander fallout from the episode. They had originally intended to just come out and call him gay. Their lawyers said that's slander. Then they wanted to say he was in the closet. The lawyers said that's slander. Then they said, "Lets just show him hiding in the closet, and then another character can say 'he's in the closet' and that became the joke for the episode.

So what this means to me is that you can generally say whatever you want, but you have to be very if you are speaking of a specific person.

Given that you gave them fictional names and fabricated some of their details, I don't think you have a huge amount to worry about, however I'd definitely include a disclaimer like you see in many books and movies; something to the effect of: "The events and characters portrayed in this book are fictional."