Dany is only 16 at the end of the books. And yy, she grows into her own. Dany controls her son, Drogon. And her other two, well, they were looking for her, their mother.
Jon himself is about 18 or 19.
I don't find her irritating at all, but more someone who grows into the role.
Still, at the end of the books we have Ser Kevan Lannister killed, by Varys' strange children and he tells him it is for someone, whom he identifies as male, who has come to rule not because he believes it is a right but because he knows it is his duty.
Dany had a vision of a man dying of grey death, in the Palace of Dust.
The letter, the letter Ned wrote is quashed, we never know what it says at all.
Is Jon Snow the child of Lyanna and Rhaegar? Who knows.