These are not in chronological order, they are organized by category.
(long post warning)
Eragon will act as mediator between Roran and Murtagh. More to help Murtagh understand Roran than vice versa. He can vouch for Murtagh’s moral code, but his choice of actions and thought processes consistently surprise him.
Murtagh takes note of Roran and Eragon’s playful affection. The arm around the shoulders that turns into a headlock, the hair ruffling, the playful shoves and punches, the hug wrestling. Murtagh’s not one to participate in such actions but it brings the shadow of a smile to his face seeing this affectionate piece of their relationship.
Roran is the broadest and brawniest of the trio.
Given Roran’s physique, Murtagh does NOT like the idea of sparring him. He will if asked, but only weapons, he refuses to spar barehanded. Even with weapons, he knows that one strike from Roran will make him see stars, briefly knock the wind out of him, or make his muscles ache. (Eragon later confides that he once wanted Roran’s broad muscles.)
Watching Murtagh and Eragon spar with swords is quite a show. Both display their lethality and mastery of the blade. They are truly in a class of their own.
Roran admits that he doesn’t like magic for various reasons. By itself, it’s not natural. Some of the effects of it cause threats to others, or disrupts the pattern of nature. He admits it’s a powerful tool and weapon, but what is within the capabilities of magicians, spellcasters and Riders is terrifying and blood chilling. His only concession with magic is when it is used for healing. He’s surprised when Murtagh agrees, understands, even validates his viewpoint. He is shocked and floored when Murtagh asks if Roran would prefer he not do magic under his roof. Roran allows healing, but "if you can do something with your hands, forgo it." Murtagh agrees saying that’s how he prefers things. This greatly helps their relationship.
Roran realizes an irony in his relationship with his cousin-brothers. He’s had to adjust to view of Eragon, accepting that Eragon has changed and grown in his power, and is no longer fully human, but is still the same man he’s known his whole life. He’s had to make concessions while wanting to hold on to what makes Eragon, well Eragon.
With Murtagh, his initial introduction to Murtagh’s existence is that of an angry, destructive, bitter traitor and war leader. As he’s gotten to know Murtagh more, he sees Murtagh’s humanity. His kindness, compassion and concern for others. His protective streak, and a ferocity that stems from love and concern for the wellbeing of those he takes into his heart. Seeing this side of Murtagh helps Roran bring his guard down around him. Seeing this side of him helps him understand why Eragon became friends with him. It makes Roran grateful that Murtagh protected Eragon when he couldn't.
With one, he tries to hold onto humanity in spite of magical changes. Tries to hold to what's left of his precious brother. The other, he sees humanity in what was thought to be a destructive force. He sees a worthy ally and someone he will not regret to call family.
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The moment Murtagh saw Ismira he was ride or die for the little child.
Murtagh gives the sweetest gentlest most sincere smiles towards Ismira. (Eragon thinks this is adorable and loves seeing Murtagh’s softer side. Roran smiles too and eventually thinks about calling Murtagh one of Ismira’s uncles)
When Ismira is still little, she goes after the items on Murtagh’s belt. Not wanting her to get into his stuff, especially his dagger or Ancient Language compendium, Murtagh buys another belt to wear during his visits so he can keep his pouch and dagger connected to his usual belt.
Roran and Katrina privately admit surprise to each other at how gentle Murtagh is with Ismira.
In a familial sense, Murtagh has a soft spot for Katrina in his heart. He also holds a high respect for her as a hostess, as family, as a lady of rank, and for what she’s been through.
During one of his visits, Murtagh teaches his family some of dances and songs he learned growing up. They are surprised at Murtagh's dancing skill and applaud him for it. (When Ismira is older she gets in on it too.) Murtagh beams at their praise. In return, the family teach Murtagh the dances and songs of Carvahall. He is deeply grateful for this. To learn about his heritage, to be included in a place he could have (should have) grown up in. It's night filled with laughter.
Murtagh is visiting when Katrina gives brith to a second child. He tries to be calm for Ismira's sake, even though he, Roran and Eragon are nervous. When the baby finally comes, Murtagh hangs back so the rest of the family can greet the baby. Roran notices and invites him to come with them. The baby boy is passed around and offered to Murtagh. He has to have a bit of coaching, but soon he is holding the newest member of his family in his arms. "Hello newling," he said quietly. He's mystified by this small human. Like with Ismira, this new child instantly earns Murtagh's protection, love and care. Roran introduces Murtagh as Uncle Murtagh to his son. Murtagh looks at Roran in disbelief. "Are you serious?" "Yes, you've more than proved yourself," Roran affirms. Murtagh maintaining his hold on the baby feels his heart melt for a completely different reason. Tears form in his eyes. He looks to Katrina, she affirms Murtagh's position in the family. Murtagh hands the baby back, trembling with joy, then puts his face in his hands hiding his tears. After a few moments, he gently hugs his cousins, his brother and sister, and thanks them for the greatest honor he has so far received.
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At some point, Murtagh tells his family of Tornac. How they met, how Tornac guided him, the lessons he taught. Some of his favorite memories with Tornac. It's hard to share through his grief, but each fact and story is accepted by his family. He even gets a comforting squeeze from Roran and a hand hold from Katrina. Roran says that "Tornac sounds like someone Father would have shaken hands with." Katrina and Eragon affirm that. Hearing that warms Murtagh's heart.
Murtagh learns of Garrow. His work ethic, the kind of house he led, his expectations of his son and nephew. His kindness, his stubbornness and pride, what would anger him. How he relaxed, his favorite things, the wisdom he passed onto Roran and Eragon. Murtagh's heart twinges with regret and jealousy that he never got to know his uncle. He notices striking similarities between himself and Garrow. He wonders if they would have clashed, or gotten along if Murtagh had been raised under him. Eragon, knowing that receiving things second hand about deceased loved ones can be bittersweet, tries to offer some comfort. Even though Murtagh didn't get to know Garrow, the wisdom Garrow passed down to Roran and Eragon, Murtagh now has too. It's partially successful, Murtagh gets himself appreciates the intent.
At one point, the cousin-brother trio visit the graveyard to pay their respects to Garrow and Marian. Murtagh and Eragon each bring a couple bouquets of wildflowers to lay on their graves. Murtagh cries, angry that he was never given the chance to meet his uncle and aunt. He says a few words to them, his wish that he had met them, that he hopes they find peace in their rest. ... That he quietly hopes his mother is with them.
Eragon apologizes to Garrow for not being able to save him. Briefly talks about what has happened. Eragon cries freely, turning into sobs. Roran puts an arm around him and pulls him into his chest. Eragon holds on as his tears flow.
After they reach the edge of the graveyard, Murtagh stops Eragon. In the Ancient Language he says, "Our Uncle's death was not your fault. I don't blame you for it." Eragon thanks him. Murtagh brings Eragon into a hug as a wave of tears come over Eragon. A few fall from Murtagh's eyes. When they part Roran puts a hand on each of their shoulders. Murtagh and Eragon put a hand on Roran's. They walk back, maintaining a level of comforting contact, united in their grief and in the comfort that they have each other.
Eragon loves seeing his two big brothers get along. Roran comes to enjoy his older cousin’s company. Murtagh is warmed and delighted to be included.
Ok but to add to all the Uncle Murtagh thoughts lately: Ismira also loving his partner and Murtagh just falling for them even harder and although it would take him a long time to get comfortable with the idea of having kids with someone, it kinda plants the seed in his mind.
