The dagger was Littlefinger's; he lost it to Robert when betting on Jaime winning over Loras Tyrell in the joust.
And of all the Lannisters, Tyrion was the most likely scapegoat; as others have noted, Jaime was famously hands-on when it came to killing, Cersei was the queen and Tywin the most powerful man in the kingdoms, but Tyrion, a man whose affliction garners him great amounts of prejudice and animosity, is an easy target. I doubt that Littlefinger could predict that Tyrion would go the scenic route to the Wall, thus enabling the encounter at the Crossroads' Inn, much less that Tyrion would be placed in a position of power over Littlefinger so soon after he had initiated the war.
"What can Stannis offer you? Onions. And potatoes, too."
- Davos Seaworth
"...but never think that means I have forgotten. The North is pretty good at rembering stuff, Onion Knight."
- Wyman Manderly
"Don't make me rue the day I made sweet, sweet love to your mother."
- Roose Bolton
"The Mountain isn't sitting on a horse anymore."
- Doran Martell
There are a couple of reasons why Renly was working on this scheme:
His own relationship with the Lannisters, and Joffrey in particular, was very poor. He (rightfully) suspected that once Joffrey took the throne, he would lose most of his influence at court, and they might eventually try to off him, in order to claim Storm's End for themselves.
Courtesy of Cersei, the Lannisters were wielding a huge amount of power over the court. Renly was standing outside that circle, and his influence was limited as a result. Knowing Cersei, he also knew that this iron ring around Robert could too easily off the king if he grew truculent. Renly and Robert may not have been that close as brothers, but the former definitely loved the latter as one loves a brother.
Being the lover of Loras Tyrell, Mace's favorite child, means Renly could exert a massive influence over the power behind the throne if Margaery were to become queen.
While it's fairly clear that Rickard did have his sight beyond the borders of the North, this does not mean he had ambitions for the throne itself. My reading is that Rickard sought to raise House Stark's position among the great houses and create a political power block to check the power of the throne. The true mastermind behind it all, however, was most likely Jon Arryn, a man with a proven political accumen.
As the daughter of the Lord of the Arbor (Paxter Redwyne's grandfather), Olenna is exactly the kind of political match that Aegon might have spurned when he let his sons marry for love. By using plural in his recollections, Barristan Selmy implies that Duncan the Small wasn't the only one to get to marry the girl he wanted, extending the field to include Jaehaerys and the unnamed youngest son.
The following is merely speculation, and somewhat black and white: Jaehaerys was purpoted to be the least martial of Aegon's sons, as well as being an all round stand-up chap. Present-time Olenna is famous for disparaging that kind of martial man, instead praising the more intellectual types like her grandson Willas.
Am I the only seeing a pattern?
If Olenna did indeed break off the match with the unknown Targaeryen, I'm disinclined to believe she'd have passed over the intelligent Jaehaerys. If the Targaeryen was more martial by nature, I could see her passing on that kind of man.
Now if we suppose that Olenna's version is fabricated, and she was indeed spurned, I could see her impatience with martial men stemming from bitterness against the man who spurned her. Hence regardless of which version is true, Jaehaerys seems unlikely to have been the Targaeryen Olenna was supposed to marry.
I think the "certain ploy" is most likely the recreation of the tale of Bael the Bard.
Even if you subscribe to the idea that Mance is collaborating with Mors Umber and/or Wyman Manderly, it's unlikely he had finalized his plans at the Wall, not knowing the players that would be at Winterfell.
Tywin got his daughter married to a king and his grandchildren on the Iron Throne by killing the Targaeryen children. What could Aegon have possibly offered Tywin to not only beat that arrangement but also offset the rather extreme risks he'd take by doublecrossing the Baratheons?
Also, the babyswitching scheme is, IMO, logically hogwash, hence I doubt such a scheme actually took place. For alternative explanations search for threads labelled "Aegon" and "Blackfyre".
Real!Aegon would be about eighteen years old by now, being born in 282 AL, whereas Jon is sixteen, being born in late 283 AL. Given that Jon Connington was introduced to Young Griff at age 5, it's quite unlikely that he is anything but Real!Aegon's age, hence he cannot be Jon Snow's twin brother.
Jaime is actually a fairly good fit for Darth Vader, though his "evil" is far more ambiguous than the fullblown atrocities committed by Vader. His path of redemption is also different: Jaime is trying to become the man he always wanted to be, but Vader steps away from the Dark side to become the man he once was.
Vader is a man completely ruled by passion (unchecked love slowly turned into a seething, endless hate against the universe). He has never craved personal power, only the means to save those he loves. He is content with taking orders as long as they give him a sense of purpose, and has no regard for laws or politics. How does any of this apply to Stannis or Tywin?