However, when Anakin turned to the dark side, Obi-Wan was tasked with stopping him, and their friendship was shattered. As Obi-Wan left Anakin to die on Mustafar, it's possible that Anakin was weeping not just for his physical pain, but for the loss of his relationship with Obi-Wan.
Anakin cried when he thought Padme's life was in danger and after he killed the younglings, but Obi-wan never shed a single tear, even after his loves death in the clone wars and Anakin's fall.
At one point when he is furiously pressing Obi-Wan down, it does look as if he is mouthing "f*ck you", but obviously we don't actually hear that in the soundtrack.
Did Darth Vader ever regret killing Obi-Wan Kenobi in Canon or EU? 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.
As he turned to the Dark Side and became Darth Vader, Anakin came to hate Obi-Wan, but never stopped respecting him. In the end, it was Vader who would take Obi-Wan's life, but it was Obi-Wan who would set up the path for Anakin to be redeemed.
Anakin does not have even the slightest bit of remorse. By the end, he feels nothing but anger. Although he feels regret for killing Padme, he still helps the evil Emperor. The film ends with Anakins standing side by side with the man on whose behalf he has committed all his crimes.
Anakin admits to Obi-Wan that he has been arrogant and unappreciative of his training, and apologizes to his master. Obi-Wan assures Anakin that he is proud of him, telling him that he has become a "far greater Jedi than I could ever hope to be."
The Jedi, with the exception of Obi Wan (and Qui Gon before he died), openly distrusted and even disliked Anakin.
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.
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.
Losing Anakin to the dark side, along with the loss of the Jedi Order that sheltered and raised him his entire life, had to have been a very difficult and painful process for Obi-Wan. It was only natural for him to feel at least partially responsible for those losses.
The Younglings Reminded Anakin of How Different He Was
The canonical comic Star Wars: Darth Vader #7 confirms the younglings' deaths caused Anakin grief, self-loathing, hatred and pain, fueling his descent even further into the dark side.
I think, just as Palpatine said, Vader's emotional connect to Obi Wan is what makes him weak when they confront each other. So, his denial of the fact that he wasn't Obi-Wan's failure per se, made it easier for him to let go of those small hidden emotional connections and bring him again to his full potential.
He sacrificed himself to help Luke, Leia and Han escape the Death Star. He didn't want Luke to become embroiled in the fight. He knew he was going to lose eventually.
This is the most well-known of the Jedi rules. Love leads to attachment and attachment leads to strong emotions, which are the path to the Dark Side of the Force. Because of this, Jedi are forbidden to fall in love. This, of course, doesn't stop Anakin Skywalker from falling in love with Padmé.
Anakin Skywalker
As Yoda considered such things to be dangerous, he thus deemed Anakin unfit for the life of a Jedi.
However, when they next met in Star Wars: Episode II – Attack of the Clones, Anakin and Padmé's feelings for one another grew into something resembling love, and their wedding at the end of the film solidified their relationship as one of the most important romances in Star Wars history.
Good question! First and foremost, Obi-Wan didn't want to have to confront and try to kill Anakin, we see this all the way until their final conflict in their duel where Obi-Wan pleads with Anakin to not make him do what he knows he'll have to do if Anakin tries to attack from the low-ground.
On a practical level, Obi-Wan did not know that Anakin had survived simply because he was isolated on Tatooine. Although Obi-Wan did not see Anakin die after their battle on Mustafar in Star Wars: Revenge of the Sith, he reasonably could have assumed that Anakin would die from his injuries.
Before he discovered Vader had survived Mustafar, Obi-wan lived with the regret of killing his son, brother and best friend. After, he regretted not killing him and wondered if he had only made things worse by pushing Anakin further into dark side and Palpatine's arms.
What Padmé knew about Anakin's previous dark deeds. Padmé was well aware that Anakin had committed dark crimes that would've started his fall to the dark side. He even confessed to her that he had massacred an entire Tusken Raider village to avenge his mother, leaving no one alive.
Anakin is a tragic hero at its finest, a man who turns evil and loses sight of what he was fighting for once his anger became too high, even choking Padme with his force abilities out of anger and pain, believing she didn't trust him after what he did to the young Jedi padawans.
Had Anakin not converted: Padme would have been killed by the Emperor before childbirth, and before Anakin and Obi wan returned from the mission to destroy general Grievous. Regardless: order 66 probably still would have happened since the army was under control of the dicator in Palpatine.