1. Jaime learns that Robert, in a drunken state, declared that Bran ought to be put out of his misery. He said this in front of Joffrey. Was Joffrey the instigator of the assassination attempt?
Well, I have no doubt that Joffrey was responsible for this. Tyrion guessed it (or concluded based on some reasoning he didn't articulate) and Jaime's recollections back it up. He thinks it was Joffrey as well. Unless some other truth comes out I'm going to assume this particular mystery has been solved. Joff is at the source of this whole conflict!
2. Jaime sees his page in the White Book. Are his gifts to Brienne and his treatment of Cersei an indication of a real desire to be a new man?
Yes, I think so. He can't be the old Jaime, not without his arm. His fighting skills is how he defined himself. Without them he needs to think of something else to do.
3. Ser Kevan has issued a pardon to the Westerlings (loc18226). Does this mean Jeyne is NOT pregnant and is therefore not a threat? Does this mean they WERE in cahoots with the Lannisters?
Yes, I suspected that all was not kosher with the Westerlings. There was that uncle that Grey Wind did not like. (Did we ever see this uncle?) The whole family was just kind of creepily nice. And dull. Perhaps Martin just didn't fill them in well enough. But I agree with Vonda that the pardon comes too easily. Tywin is not in the habit of pardoning anyone for treason, so why were the Lannisters so quick to pardon the Westerlings?
Some Westerlings did go to the Red Wedding. Do we know what happened to them there? Did they survive?
4. Stannis and Melisandre are rumored to have sacrificed a man to come to Eastwatch (location 19070). Was this Davos in punishment for smuggling away Edric Storm?
It's odd that Davos is not with them on the Wall, but perhaps Stannis left him back at Dragonstone to, as it were, rule the "kingdom" in his absence. Since they have ended up coming to the Wall Davos clearly succeeded in convincing Stannis to follow his advice. Which in this case happened to overlap with Melisandre's thoughts. She saw - and showed to Stannis - snow and war in the fire. I don't think Davos was the man sacrificed.
5. Did Mance have the real Horn of Joramun? Was his expedition into the mountains a success?
I have no idea! The Horn of Joramun would collapse the Wall, right? And allow the Others and the wights to easily invade Westeros, right? My theory, I think I wrote it before, is that the reason Mance assembled the wildlings and they are marching on Westeros is because the are being squeezed out by the Others (and whatever else is out there). And they need to place to go and be safe. So they have to get to the other side of the Wall. Why would Mance want to destroy the Wall and unleash the Others? Perhaps he's actually trying to protect the Horn from being used?
6. Arya the BAD-A$$! She is definitely the only character who is getting to become her own childhood fantasy! Is she making the right decision to abandon Westeros to become a Faceless Man?
Finally a Stark taking some action! And not being killed! Sheesh! I think she definitely made the right decision. In fact, she should have come with Jaqen when he invited her. She's lost time, witnessed further trauma. And is, once again, all alone. At least she would have had someone with her before. But here we are. I think Arya as a Faceless Man/Assassin will be awesome. (Unless Martin kills her.)
7. What will become of Sandor, assuming he lives? Will he take up service with some Lord?
My guess is yes, he will survive. Otherwise his whole story arc would be kind of pointless. But what can he do? I don't know that there's any Lord who would take him into service. Nobody loyal to the Lannisters would. I don't think Stannis would. The Hound doesn't have enough honor - certainly not the honor Stannis seeks. Though Sandor is quite honorable in his own way. If you take all the killing out of the equation. But does he have some kind of guilty conscience over Mycah? He tells Arya to stop saying his name. I think the only thing Sandor can do at this point is join some church, become a priest.
8. Should Jon have accepted Stannis’ offer to become Lord of Winterfell? Would this appointment, along with the marriage to Val, have accomplished anything?
No, I don't think he should have accepted the offer. For many reasons. One: he swore an oath to the Night's Watch. I can't imagine Stannis would actually encourage the breaking of an oath. Or is Stannis selective in these things? Two: he'd be too indebted to Stannis and Melisandre and the cost, I think, would be too high. I don't trust them, certainly not Melisandre. Three: it would make him look bad in the sense that he's not really entitled to that land because he's a [illegitimate person]. And who is Stannis anyway? A King without a Kingdom, he's nobody. But we know that Robb legitimized Jon - and there are people out there who know this. Jon doesn't need Stannis. His own brother has already made him a Stark. (Jon just doesn't know it yet.) That is a much more legitimate path than anything Stannis has to offer him.
9. Tyrion, the BAD-A$$! Was Jaime’s revelation about Tysha (so long in the past and undoubtedly the lie Jaime thought about a few weeks back) justification for his lie to Jaime and the killing of Tywin?
Well...I also wish Tyrion hadn't lied to Jaime. Does Jaime believe him? I guess we'll have to wait and see. As far as killing Tywin - well, finally the Lannister body count grows. I mean for crap's sake! Tywin was a fascinating character. I think it's obvious that if it was up to him this war would not have been fought. He was angry at Joffrey for killing Ned. But he certainly doesn't fight clean. His part in the Red Wedding was deplorable. And I think the gods (whichever gods) are doling out punishments. Joffrey and Tywin for Robb and Catelyn. And Tyrion escaping. Can you imagine Cersei's rage?!

Now let's hope for similar fates for the Freys and the Boltons.
Now how do we feel about Varys actually arranging Tyrion's escape? I've always liked Varys. I hope ultimately he's a good guy; he's certainly acting like the good guy here. But, of course, trust no one!
10. How long has Shae been with Tywin? Since the trial, or before?
I'm guessing...she's been in Tywin's service from the get-go. Another whore he hired to teach Tyrion a sharp lesson. And to keep tabs on him. It does explain why Shae was so fearless while in King's Landing. Foolishly so, not caring about secrecy and keeping her head down. She acted like she was invincible and she probably was, knowing Tywin would protect her. Can Tyrion ever trust another human being again?
11. What has Maester Aemon discovered about the sword Stanis bears?
I guess he discovered that Stannis' sword is not magical. Melisandre won't like that! I hope Maester Aemon watches his back.
12. Jon Snow, Lord Commander of the Night’s Watch! Can he handle this responsibility?
I didn't love this chapter. A little too Hollywoody. But I don't mind the outcome. I'm surprised people like Marsh actually backed him. Jon is a child! And they know he's spent time with the wildlings. So why do they trust him? Or do they just know that the alternative is not an option?
Now some questions I have.
Why is Sam not allowed to tell Jon that Bran and Rickon are alive? Surely that secret would be safe with Jon! And it would give him some peace of mind to know not all of his brothers are dead.
Who is the mysterious guide? It has to be an Other, right? And possibly Benjen, right? If both of these are true - how can an Other not be a murderous zombie? Does it mean Others have free will? Are there other (!) Others like him??? Or if he's not an Other, could he be the undead like Beric and Catelyn?
Speaking of Catelyn: no question about the Epilogue?! I looooved seeing that Frey doofus get caught and then hanged. And seeing the undead Catelyn. Yeah! And that little twerp Frey, the pimpled one, already hanging. Walder Frey will be annoyed. Too bad!

I sure hope Catelyn goes on a few bloody rampages.
And Lysa/Littlefinger/Sansa. So we know that it was Lysa Littlefinger deflowered, not Catelyn. But he thought it was Catelyn! Now I can't remember already if this was information he heard Lysa say or not? Or is it just Sansa who knows and Littlefinger is still under the impression that he and Catelyn were lovers. At least it does show one thing: Littlefinger wasn't spreading lies intentionally about it. He actually believed that he bedded Catelyn.
And then I loved seeing Littlefinger throw Lysa out of the moon door. She always loved that thing too much! I hope Sansa watches and learns.