Littlefinger has Joffrey killed in order to create even more havoc and just enough of a commotion to "free" Sansa. He conspired with his lover, Lyssa Arryn, who in turn murdered her husband as a way to get this whole ball of wax started. They talk about it right before he pushes her out of the Moon Door, thereby claiming status as Protector of the Vale as father-in-law to the weird kid.
And with Tyrion killed for his perceived crime, that leaves Littlefinger free to marry Sansa and claim Lordship of the North as well. But then Tyrion gets away.
Outside of the books, the leading theory is that Coldhands is Benjen, but... apparently prequel materials also point to some other possibilities.
The real question I think holds the key to everything is: Who are Jon Snow and possibly Tyrion?