Beyond that, I still don't understand half of the most important characters motivations.
Why does Tyrion want to help the mother of dragons?
He doesn't. He wasn't exactly going there for her sake but to escape Westeros after he did the deed. Varys wants him to go with Dany so he did since he didn't have a choice at that point. He's a fugitive with no money so he can't do the things he loves so what else would he do worth the risk of being caught? Dany can protect him if she deems his information worthwhile. He's got no money, no friends, people looking for him with Lannister spies all over the world, and while he doesn't originally want to go to Dany, it's a way for him to either get it over with or get some protection and possibly repay the sins his family committed.
Why would Sansa agree to marry into the family who murdered her mother and brother?
Because that's what Littlefinger told her to do to reclaim the North in her family's honor. She's not going to take it over by force, but by cunning and her best option is to marry into the family and then make her moves. It's not like she wanted to do this as she clearly showed us she didn't when LF told us. LF is the one making the moves here and having a Stark in his corner is a lot of power. Sansa is going to grow and learn to play his sort of game compared to the moves his family made that only revolved around justice in the eyes of the law, but justice rarely works that way.
Why does Jorah think that returning Tyrion to Dany will earn him favor?
Because he doesn't know that Tyrion is a fugitive at first and thinks of him only as one of the enemies that took the throne from Dany so he'd be a good prize for her, whether it be as a trophy or for information since he's privy to Westeros and his family's workings. He's a fool blinded by love and just got kicked out of the family so to speak so he's desperate to win her back. In his eyes, bringing her a trophy is better than nothing.
Why does Dany and Cersei repeatedly make incredibly obvious and stupid mistakes in playing the "game"?
Because they're not perfect? Why does the President make mistakes in real life? Why did Frank Underwood make mistakes in House of Cards? Dany is a young woman with no experience in leading so she has to learn as she goes. She didn't get to learn from her father and family but lived life on the run so she's bound to make mistakes, especially in a different culture that has a lot of nuances Westeros doesn't have.
Cersei makes mistakes because she's blinded by one thing, the prophecy and how she's bound to lose her family yet she doesn't realize she's losing them because of her own actions. It's sort of self-fulfilling so she thinks she can make moves to prevent it, but those moves are what causes her family pain. She's blinded by her own ego and isn't looking out for the kingdom, but her family.
Mostly everything in the show feels like some sort of contrivance to bring in the major characters all together on screen at once. I'd love for someone to try and break down my questions with reasonable answers. I'd be more than happy to listen.
