1. Who killed Jon Arryn?
What is the answer to the mystery that drove Ned's actions in Season 1? How did one of the first corpses on the show happen to die?
Wasn't it stated (or implied at least?) that Cersei and the Lannisters did because he figured out her kids weren't the King's? Ned figures this out right before he goes to confront her..iirc, I also have not had time or ambition to rewatch yet.
2. Who sent the guy with the dagger to kill Bran while he was in his coma?
This drove a lot of what Catelyn did. It resulted in Tyrion's arrest, without which Bronn would never have come into the story. Littlefinger suggested in one of his last conversations, that event made Bran who and what he is. So who was responsible for it?
I can't remember and don't feel inclined to rewatch, but I cannot for the life of me recall any indication that the award-winning writing on this critically acclaimed show ever bothered to finish its first ever story.
I believe this was also Cersei to protect the little secret Bran stumbled on..ie: Finish the job Jaime started when he pushed him out the window.