Lotd Randyll's holdings are in the Reach. It would be political suicide for him to declare for another liege and against the Tyrells.. I don't see him as necessarily loyal to them, though. He may stage a coup to usurp the Tyrells, or maybe even the Iron Throne, if the situation really gets messed up, with an invasion by Dany added to Aegons's and Stannis coming back from the North.
Littlefinger is fostered with the Tullys, where he's exposed to how the upper crust really lives, in comparison to Schloss Baelish. Instant envy. He falls "in crush" with Cat, gets informed in no uncertain terms that he's not good enough for her. Gets royally miffed when Cat is affianced to Brandon Stark, to the extent of challenging him to fight for Cat's hand and is nearly killed. The humiliation continues to eat at him. As lord of that tiny fief he doesn't have the means to extract revenge so he sets out to gain enough wealth and power to accomplish his ends. Theon may be a hostage but he's treated nearly as well as the Stark kids are. Pals around with Robb, takes sexual advantage of the miller's wife, looks down his nose at Jon. He may be a Greyjoy but he's given responsibilities in Robb's war. Then when he goes to Pyke he again takes advantage of a woman of the lower social orders (the captain's daughter), and attempt the same with his sister, whom he doesn't recognize but again considers a commoner. He's resentful of Balon giving him a lesser command than Asha got, even though he's inexperienced. Arya is written as a special character. She defends the weak, Mycah from Joff, Sam from the Braavosi bravoes, the baby named Weasel, among others. She avenges evil, as with Chiswick. She punishes Dareon (sp?) for abandoning Sam, Gilly, and Aemon. A few of her kills have been iffy, as the guard at Harrenhall, but most have been necessary. Sandor says that he killed his first man at age twelve, but Arya beats that by three years. How can you not love that? Dany being "Blood of the Dragon" is a bit facetious, but it's what has been drilled into her by Viserys and she thinks of herself that way. The original post calls for opinions, and those are often not 100% objective.
Jaime...light gray. His one really bad deed was throwing Bran out the window. He's done some good things since, and he saved King's Lading from being incinerated. Tywin...evil. Wiping out both the Reynes and Tarbecks to the last suckling babe is enough, but him loosing Gregor and Amory Lorch against the Riverlands puts the seal on it. Tyrion..mid-gray. He's done some fairly bad things but mostly tried to do good, at least until he was unjustly convicted of regicide. Cersei..evil. Sexually abusing her baby brother was just the beginning of her arc. Age 9, pushing her playmate down a well to drown, plotting to kill her husband, causing the deaths of numerous dwarfs, sending Falyse Stokeworth to Qyburn are more low-lights. Petyr..evil. Eaten up with envy of the great Houses, especially the Tullys and Starks, he contributes to a devastating civil war to get vengeance. Varys..at best, mid-gray, at worst evil. Working to overthrow the realm to install his own candidate for king. Uses up dozens ,if not hundreds, ofchild slaves (whose toungues have been removed) in the process. Theon..dark gray. He's basically a privileged snot who has done evil deeds but rescued Jeyne Poole from Ramsay and has suffered for some of his villainy. Victarion...gray. If he weren't such a cartoon he'd be evil. Aeron...just a religious wackadoodle. Bran...still in the larval stage. Has done nothing good or bad, may go on to achieve greatness. Arya..beyond good or evil, she's the personification of Divine Retribution. Mere mortals are unfit to judge her. Stannis...light grey. Overall he's mostly done good, but he's too rigid and self-righteous in his judgments and punishments of others. Daenerys..light gray. Her motives are mostly good but she shows bad judgement and is sometimes overly cruel. But then she's Blood of the Dragon and that comes with the territory.
I don't recall Selmy ever saying that Ned was a particularly good fighter. Maybe someone could cite the passage? Jaime had nothing to prove as a fighter and it's doubtful that he fought for fun. In tourneys, yes, but other than that it was strictly business. If he wanted to fight Ned it's because he wanted Ned dead, which would have been the result of a fight between them.
The first paragraph has been answered. As to the second, yes, he's very ambitious, not to mention one of the smartest men in the North. I'm pretty sure he'll be working at getting a marriage between his grand-daughter and whoever the heir to Winterfell is, Bran or Rickon.
He was dead even if he hadn't married Jeyne. He never would have made it to the Twins alive to marry whichever ferret-faced Frey was chosen for him. The difference would have been that the Freys might not have been involved in his death
Tywin pretty much admitted that he was behind it in a conversation with Tyrion. His did say that he disagreed with the Red Wedding, that the best plan would have been an arrow from the woods flanking the road to the Twins. It's pretty clear that Tywin had already suborned Roose Bolton, who sent a large part of Robb's army to be destroyed at Duskendale, and between Tywin and Roose they worked to turn Lord Walder to the Lannister side.
Well, there's no evidence that Valyrian steel is especially effective against the Others. Dawn may be, and dragonglass has been shown to be effective, but Valyrian Steel wasn't around the last time the Others attacked. As to "they" trying to kill Jon again, it was a small group of mutineers that attacked him, and it's not guaranteed that they will survive the outrage that their actions incite. I can see Ser Wun Wun mashing them to a pulp on his own, not to mention all the Wildlings standing around who like Jon better than they do most "crows".
There's a scene before the stabbing where Jon, Marsh, and others are under the Wall in a freezer-type storage area that has hams hanging. I like a scenario where he's brought there and returns to life amid "salt and smoke", which is how hams are treated for prerservation. Thus becoming AAR. Mel glamours one of the corpsicles Jon has stored in an ice cell to look like Jon and that's cremated with full ceremony, thus there's no more Lord Commander Jon Snow.
There have been a few discussions about the conversation with Kevan. There are three points brought out: why would Varys lie to a man he's about to kill, why would he say anything at all to that person, or he was speaking for someone other than Kevan's benefit, either a listener or for the "little birds" to report back to. I don't expect many players in the Game to tell the truth. Maybe the Elder Brother or Septon Meribald.
I think the OP takes people at their word too easily. Varys is a notorious purveyor of half-truths if not outright lies. He's doing what he does "for the realm", but his idea of what the realm is almost certainly means something different than the casual listener would assume. It's Ser Shadrich, not Ser Creighton, who is looking for Sansa, and he's doing it for an expected reward, not for pay. Again, we don't know how much truth there is in his statements. I suspect that he's playing his own game.