also I'm very impressed at how every single one of the countless new characters introduced in this episode were perfect. even if this show's writing leaves a little to be desired recently, I have to give casting an A+.
the best episode I've seen in a long time. possibly since season 1 IMO.
would have been a 10, I'm giving it a 9 because of weird timing - some scenes were too drawn out where others were cut too short (the scenes with the Reeds seemed a bit awkwardly short considering it was their time to be introduced, and I'm also a little peeved they cut the discussion of marrying Willas from the Sansa/Marg/Olenna scene)
I wouldn't give the Lannisters full credit. They played a part, yes, but a HUGE part of it was timing and bad luck on the part of the Starks. Had Theon not taken Winterfell, the Starks would still have the Freys, perhaps the Boltons (I'm sure Roose just wanted to be part of the winning side, and he said himself it was Robb losing Winterfell that made him turn sides), and would still have Jaime to hold over the Lannisters' heads. Though I do sort of think Robb was doomed from the start - I have a feeling that even if Robb married Roslin and they hadn't lost the North, those who betrayed him would have found some other reason to do so the second the North campain was on shaky ground - that's where timing plays in. Compared to the Starks', the Lannisters' downfall has been (and continues to be) much quicker and more violent. As Tywin was a huge player in the Red Wedding, and the Lannisters were on almost as equally shaky ground as the Starks towards the end of Robb and Cat's arc, if Joffrey's wedding had happened the slightest bit earlier it's definitely plausible that the Lannisters would be in the Starks' place right now instead.
To answer the Kings Guard part of the question, I would say it's Rhaegar's obsession with prophecy that lead him and in turn the KG to be very protective over Jon. Once he had a child that was the literal "song of ice and fire" I'd imagine he'd do anything to protect him, including sending the KG off to the tower, even if they needed them in Kings Landing.
As to why they followed Rhaegar's orders and not Aerys: though the KG's job is to protect the king, it without a doubt extends to the whole ruling family, and especially with Aerys' madness and the impending sack of Kings Landing I don't think it's too farfetched to imagine that they turned from protecting Aerys to his heir Rhaegar, and then followed Rhaegar's orders to protect Jon (I'd even venture that with the fall of the Targ dynasty in KL, Rhaegar's new son in the middle of Dorne seemed like the most able to protect out of all the Targaryen heirs, so to make sure that House Targaryen carries on (pretty much the job of the Kings Guard) it even makes sense logically that they would leave KL in favor of going to the tower of joy)
shhh don't even talk about them not casting val! i refuse to think about it after what happened some of my other favorite minor characters
but yeah I agree it looks like val's going to have some sort of role in the future, they may treat her like the reeds and only cast her when absolutely necessary (so maybe for next season when we get more into the wall politics, since she's only occasionally mentioned through most of ASOS and from what I understand that probably wouldn't work logistically if you're hiring a full-time actress). though I will be missing the little bits with val they could have had in this season, like jon initially seeing her from afar, and potential interactions she could have had with Mance and other important wildlings.
edit: we also need Val because her and Gilly being BFFs at the wall is something I must see. but thankfully this can wait until the ADWD portion of the show as well.
Jon leading the battle on the wall. he's always been one of my favorites, but at that moment I felt the most immense sense of pride for him. I actually had to read a few of his speeches to his men a couple times for them to really sink in and convince myself that this was the same Jon Snow from AGOT.
and sort of in that vein, Jon turning down Winterfell as well. I know it's a little broader than you're asking for, but the few passages, from the flashbacks between him and Robb and learning from such an early age what "bastard" means and how he'll never have Winterfell, to his dream of the crypts and the Kings of Winter telling him he's not a Stark, and just generally reacting to Robb's death, hit me really hard. Especially when he remembers Robb telling him as a kid he'd never be the lord of Winterfell, but then he refuses Winterfell out of respect for Robb and his siblings, not spite or self-pity or anything else. For me that's the moment he really comes into his own, and though I initially felt a lot of sympathy for him after his inner thoughts, again it quickly changed to pride for him when he simply used that past to build and establish who he was as a person once and for all.
Lastly, Sansa's escape from Kings Landing. it's just so moving and emotional, And while during her stay I think she was always holding out hope that Robb would come, and immediately after his death she was mourning but probably still shocked, at that moment she realizes she's truly on her own and everything comes shattering down.
for Lady, I think it more so represents how Sansa leaves Winterfell with this idealistic vision in her head of Kings Landing and court life, but Lady is killed soon after and that sort of plants the seed of her realization of the truth behind the Lannisters, so it's sort of symbolizes her idealism being killed as well. A "Lady" is everything she aspired to become - her picturesque view of what her future in the south will be - which is soon figuratively killed as her direwolf literally is.