(1) The third dragon rider is one of the hardest predictions to defend with real substance, but Tyrion is my guy for 3 reasons. First, I think there's a very strong chance that in the books Tyrion will be proven to be a Targaryean rather than a Lannister. Second, in both the books and the show they emphasize how much Tyrion has always loved dragons since he was a little boy when he wanted to ride one. Third, he is the best and most beloved character on the show.
(2) I think the show is working on a big Stark Reunion and don't expect any real infighting there. They really don't have enough episodes to fight each other and the dead.
I don't think that Tyrion will be a rider. The books made reference that Aegon and his sisters could ride the dragons because of their dragon blood. Dany has dragon blood. But in season 1 Tyrion got burnt by candle wax when playing a game with Shae.... He's a wimp when it comes to heat.