Look I'm going to say this as someone who would take the opportunity to knock Arthur's lights out in a heartbeat, it's unfair to look at certain scenes where Merlin is upset and say that Arthur didn't do enough to comfort Merlin or didn't handle the situation properly
From Arthur's perspective, he is a prince who has led his men into battle multiple times, has fought in various duels and tournaments and has overall seen a lot of death. He's lost comrades, he's watched enemies fall, he is used to thinking of death in an almost casual way. He didn't know any of the details surrounding Merlin and Freya's relationship, but he recognized that Merlin hadn't smiled in days, and he wanted to see Merlin smile. He didn't want Merlin to be sad. He didn't know why exactly Merlin was sad, he just knew he was so Arthur did what usually works-banter. Now, should that have worked? We could talk in circles. People are allowed reprieve during grief, it's not all dread and doom sometimes you do smile at stupid shit after someone you love dies. But it's understandable to look at that final scene and feel like it cheapens Freya's impact as a character.
As for Balinor, sad. Heartbreaking. Made me cry, tbh. But Arthur had no idea that was Melrin's father. In fact there's a whole scene dedicated to showing how distant Merlin really is from Arthur and how he perceives their relationship at that point and it's actually Arthur who reaches out to Merlin only to be shut down. From where Arthur is standing, Merlin is upset from the minute they start their journey and then a man dies in his arms and Merlin is even more upset. Rightfully so! So Arthur tells Merlin what he knows; he tells Merlin what he tells his brothers in arms. This is the same sentiment it's very likely Uther instilled in him. And this moment between them feels gut wrenching. This is a man, preparing to die, telling one of his closest confidants not to cry. "No man is worth your tears" is not just referring to Balinor in that moment he is referring to himself. He's telling Merlin not to cry over him.
Like look hate on Arthur all you please I'm usually on board but you have to give the man credit where credit is due