Maybe the key thing is warg + Targaryen blood? In which caseJon FTW!
Perhaps.
AFAIK Tyriondoes anyone know?has shown exactly zero signs of being a warg, and I'm not sure where the theory of his having Targaryen blood comes from...
Dany isn't much of a warg either. As for Tyrion's parentage -- there was stuff like Tywin telling Tyrion that he can't prove Tyrion isn't his son ('Men’s laws give you the right to bear my name and display my colors, since I cannot prove that you are not mine.') and tales of Aerys taking certain liberties with Tywin's wife. I don't believe it myself -- that'd be one too many secret Targs running around.