Obi-Wan apologizes for what he did to Anakin, but Vader assures him that he killed Anakin, not Obi-Wan. He then goes on to proclaim that he will destroy Obi-Wan in the same way.
“You didn't kill Anakin Skywalker. I did.” This allows Obi-Wan to finally let go of all his guilt over Anakin's transformation into Darth Vader. It allows Obi-Wan to resume some kind of life, but it's a tragic reminder of how Anakin's fate is captured behind the black mask.
Though Obi-Wan's "I have the high ground" line has become something of a meme since the release of Star Wars: Revenge of the Sith, it remains one of the best lines in the prequel trilogy.
He does. Right at the end. With Luke crying over him and Vader sensing his anguish and pain he had inflicted on all those who had cared for him.
Obi-Wan argued that the minute Anakin turned to the Dark Side and became Darth Vader, Anakin Skywalker ceased to exist and therefore Vader did, metaphorically at least, kill Anakin. This notion is stressed in other Star Wars media as well.
Yes, when Darth Vader turned back to Anakin Skywalker and sacrifice himself to save his son, he dies and Obi-Wan uses the force to connect with Anakin's spirit. In that time Anakin apologizes to Obi-Wan, desperately asking him to forgive him for everything he has done to him and everybody over the years.
David Porter provides some great philosophical context to why Obi-Wan would not regret leaving Anakin alive, as it was obviously “the will of the Force” that Obi-Wan be unable to finish him off, and “the will of the Force” that Anakin live on to kill Sidious himself in the future.
Darth Vader hates Obi-Wan, not because he blames him for his fall to the Dark Side, but because he turned Padmé against him and destroyed his body.
In the material around the film from the Legends timeline, it's established that by the end of Star Wars: Episode III - Revenge of the Sith, Kenobi was one of the characters who knew Anakin's Sith name was Darth Vader. However, what he didn't know was that he was still alive after Mustafar.
Update: So apparently Hayden Christensen said in the Q&A yesterday in Toronto that there will always be a little bit of Anakin in Vader, and that line was Anakin trying to absolve Obi-Wan of guilt.
Anakin Skywalker: [shouts] I HATE YOU! Obi-Wan: You were my brother, Anakin! I loved you!
In the story, we learn that Obi-Wan took on the name Ben because it's a nickname given to him by an old flame, the Duchess Satine Kryze. He takes on the name because it still has emotional resonance for him.
Darth Vader only learned he had a daughter in Return of the Jedi - but there's no evidence he realized she was Leia before his death and redemption. Darth Vader may have never known Princess Leia was his daughter in Star Wars and never cultivated a relationship with her, even when he was a Force ghost.
learn how Vader felt upon striking down Kenobi. from Yoda, rather than feeling relief. or vindication at finally destroying his old master, Vader, or rather Anakin, was instead. overwhelmed with utter loneliness and sorrow, having killed one of his last. remaining links to his former life.
Over the years since the Youngling massacre, and even sometime before, Darth Vader has regretted killing the Younglings, recognizing that it was the most terrible thing he had ever done.
The choice to leave his mother at a young age continues to haunt Anakin throughout his life. He is plagued by nightmares of her and visions of her fate. When he eventually saves her from a group of Tuskens on Tatooine, his blind anger at her dying state consumes him.
If you are asking about Vader post-Mustafar, then no, she doesn't. Padmé doesn't seem to know Obi-wan cut off his limbs and left him to burn alive, Obi-wan didn't believe Anakin to be alive and Anakin's surgeries were still happening as Padmé died so there was no way for her to know.
Giving in to his feelings, Anakin cuts off Mace Windu's hand, giving Palpatine the opportunity to kill him. Anakin regrets this almost instantly, but the thought of Padme was stronger than his remorse This is the moment Anakin officially became Darth Vader and led to serious issues in the Skywalker Saga.
Darth Vader hated Obi-Wan Kenobi because he hated himself. This started when he thought that Kenobi was the one that poisoned Padmé into turning against Anakin when he turned to the dark side. But the truth was that Anakin was merely projecting his own self-hatred toward Obi-Wan.
He explained to Luke, “I took it upon myself to train him as a Jedi. I thought I could instruct him just as well as Yoda. I was wrong.” His guilt was apparent in Revenge of the Sith, when he explicitly told Anakin in the heat of their duel on Mustafar, “I have failed you, Anakin.
In Bloodlines, Leia stated that she does not forgive Vader, and isn't convinced of his redemption. Surely, she spoke to Luke about how he was able to pull Anakin back to the light. Luke was able to connect with his father before he died, and forgive him for all the bad things he had done. But Leia can't.
Theory 1: Leia Doesn't Remember Ben Is Obi-Wan
Throughout her encounters with Kenobi in the series, he refers to himself as Ben. The most straightforward explanation would be that Leia knows the person who rescued her is Ben, and never connected the dots that Ben is actually Obi-Wan.