And I'm still trying to figure out who could have taught River how to fly the Tardis.
Here's some thoughts on that question that I posted to a mailing list earlier today:
River is from the 51st century. So is Captain Jack Harkness. And the Time Agency is active in the 51st century. (We know this, because Jack worked for them.) No, I'm not suggesting that Jack knows River; it's a big universe and a big century. Instead, I'm going to suggest that the Time Agency
could have been a front by the Time Lords during the Time War. What if the Time Lords were providing information to the Time Agency, letting the Time Agency either take care of small brushfires during the Time War? Or what if the Time Lords wanted the Time Agency as a kind of temporal cannon fodder? Another possibility is that the Time Agency got their hands on a wrecked TARDIS and figured out how to work it.
But if she were trying to make the Doctor jealous, then I don't know who it could be. The Doctor doesn't
have romantic rivals. Unless it
is Jack, but not the Time Agency Jack but the
immortal Jack who has lived through from the 1880s to the 51st-century.
The completely-not-going-to-happen option would be Compassion, who was the Doctor's TARDIS in the novels. It would take too long to explain, and it's really really not going to happen. It's not even a possibility.