What role does religion serve in the lives of the novel's major players?
A Storm of Swords contains characters who worship a variety of religions, and the characters themselves represent all degrees of religiosity, from the highly devout to the completely irreligious. Religious beliefs, however, are rarely a motivating force, with one notable exception: Melisandre. Melisandre is a priestess of R’hllor, the god of a religion that developed in the east in the world of the novel. It isn’t always entirely clear whether she believes that Stannis is truly the messianic figure Azor Ahai or whether she is manipulating him for her own ends, but she does appear to be genuinely devout. According to her religion, a battle is taking place between the forces of life and death (or light and dark, as she sometimes frames it), and Melisandre’s belief in the reality of this battle motivates all her actions. For her this conflict is of paramount importance, and as she tells Jon Snow, it is the one battle that matters. Beside it, all the power struggles for the Iron Throne are irrelevant.
But for most of the other characters in the novel, religion remains in the backgrounds of their lives. Though Stannis has converted to Melisandre's religion, for instance, it's evident that he does so more because he thinks it will help him win the throne than because he's truly invested. It's not even clear whether he believes Melisandre much of the time. Thoros of Myr, who is a priest of R’hllor, seems to use his religion to resurrect Beric Dondarrion several times, but even so, his chief concern is the Brotherhood Without Banners. His religion acts as a tool for him, but it's not a motivation, at least not outwardly. The Starks are among the more religious characters in the novel in that we see them pray to the “old gods” at times, and the same is true of Jon Snow. But none of them follow any religious precepts that dictate how they live their lives. Instead, religion seems to be more of a cultural matter with them in that their religion distinguishes them as being from the North. At the other end of the spectrum are the Lannisters, who don't display any religious piety at all. In fact, both Tyrion and Jaime mock the gods at times and are indifferent to religion, if not contemptuous of it.
What portrait of war does A Storm of Swords paint when considered in light of the motivations of the various kings and leaders?
The book presents war for the most part as a cynical and pointless pastime, fought primarily by opportunists and men of power. While battles may accomplish short-term strategic goals, they also breed an endless cycle of violence that has no realistic endgame. Some of the family grudges we see in the novel stretch back generations, for instance, and give no indication that they will ever stop. In this context, various rulers try to gain control of Westeros for a combination of selfish but ultimately unconvincing reasons. It's never clear how ruling Westeros would benefit Tywin or Cersei Lannister on a personal level, for instance—power certainly doesn't make either happy—and instead they seem to want power simply for the sake of power. Stannis falls into this camp to some degree, though he also feels he's owed the Iron Throne. He feels it is his according to the law of succession and he deserves it, and that's why he fights for it. Daenerys wants to conquer Westeros partly because she feels it is her birthright and partly to get revenge for the crimes committed against her family. But she doesn't even remember Westeros since she left when she was still very young and she has no real personal ties to any place there. Robb has perhaps the most sympathetic motivation. He fights to keep himself and his northern countrymen from being ruled by tyrants like the Lannisters and to avenge the death of his father. With these motivations underlying the battles and horrific violence we see, the novel suggests that war is not about right or wrong, or about fighting for one form of government over another, it is foremost about personal egos.
Romantic love influences the actions of several characters. How does love affect the decisions made by these characters?
In a few cases in the novel, romantic love leads characters to put themselves at serious risk. Jon Snow breaks his vow to the Night's Watch, for instance, by carrying on an affair with Ygritte. His love for her is a distraction in that it makes it hard for him to focus on the mission Qhorin Halfhand gave him. Although he still manages to maintain his loyalty to the Watch and even fight courageously against the wildlings later, it still creates an emotional conflict in him that makes all these actions much harder. Tyrion makes the risky choice of bringing Shae to King's Landing because of his love for her, even though he knows doing so could have serious consequences for him and even worse ones for her if Tywin or Cersei were to find out. That decisions is a distraction for him as well, as he faces the added, and very stressful, work of keeping Shae secret and safe while he tries to outmaneuver Cersei. Ultimately Shae becomes a liability to Tyrion and even testifies against him at his trial. Perhaps the most significant case of a character putting himself at risk is Robb Stark, who breaks his promise to the Freys to marry one of their girls because he falls in love with Jeyne Westerling. Everyone, including Catelyn and Robb himself, knows it's a disastrous strategic move that could lead to the undoing of their whole cause if the lose the Frey's loyalty. Of course it proves even worse, as the Freys choose to murder Robb and his bannermen at the Red Wedding.
In other instances, love influences decisions in other ways. Petyr Baelish's plot to murder Joffrey and abscond with Sansa would likely never have taken place if not for Petyr's love of Catelyn. It seems as if he makes Sansa into a substitute for Catelyn, who he was never able to have a real relationship with. Those feelings appear to have played a role in his killing of Lysa, who as Catelyn's sister was Petyr's first stand-in for Catelyn. In Daenerys's storyline, her relationship with Ser Jorah becomes too complicated to sustain. She knows he's in love with her, and his love intrigues her but also makes her uncomfortable. Her strong feelings for Ser Jorah are the reason she feels so deeply betrayed when she learns he used to sell information about her. There is no question at this point that he is loyal, but even so, it's too deep an emotional would for Daenerys to bear. She exiles him as a result.