Dany has her uses, she's just really lame to me. She can't really do much until those Dragons of hers have reached maturity. Tyrion's inclusion on their little journey may be up for debate, especially since Cat was willing to get him executed even AFTER he showed her how stupid a person had to be to make an assassin use a weapon that directly tied the kill back to them xD I think in the show Tywin actually LIKED Arya because she was really clever and had some intelligence to her. The only problem is probably in Cersei's perspective because she isn't easily intimated or reeled in. Tywin's main concern is always the legacy of his family. If he sees that Joffrey chooses at least ONE Stark girl, I think that'll be enough for him, but he may urge at least one child as soon as possible. Lannister's have enemies. Joffrey sitting on the throne just paints a bigger target on his back, and he needs to leave a child to carry on his name sooner or later.

Brann and Rickon could have managed to escape in the chaos with some help, and reunite with Arya on the way to King's Landing, since they may already be marching for Winterfell. YES to Syrio being alive! Oh, but wait, did you want Arya to ever encounter Jaqen eventually and undergo that training, only to TOTALLY screw him over and try to leave later? Assassin Arya would be super dope.