Obi-Wan Kenobi didn't kill Darth Vader (Anakin Skywalker) because he couldn't bring himself to murder his former friend and brother, viewing Anakin's near-death state as a consequence of their duel, not needing a final blow. Later, during their fight on the Death Star, Obi-Wan let Vader strike him down as a sacrifice to allow Luke Skywalker to escape, drawing Vader's attention and fulfilling his role as a guiding Force spirit rather than a physical warrior, as revealed in canon.
Obi Wan couldn't kill Vader because he always thought of him as a brother and someone he cared about. Also him not taking his life is in line with what the jedi believe. If he had taken his life he wouldn't be any different than Vader.
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.
The saddest Star Wars deaths often involve tragic heroism, lost potential, or poignant goodbyes, with popular choices including Duchess Satine (Obi-Wan's lost love), Clone Force 99's Tech (self-sacrifice for family), Kanan Jarrus (heroic sacrifice for Hera and Ezra), Padmé Amidala (fading hope for Anakin), Han Solo (betrayed by his son), and Clone Trooper 99 (innocent, selfless heroism). These deaths resonate due to their emotional impact, the characters' significance, or the broken promises they represent.
No, Darth Plagueis is not Anakin Skywalker's father; Anakin had no biological father, being born of the Force itself in response to Plagueis's dark side manipulations, with Palpatine's tales of Plagueis's power over life being a manipulation to turn Anakin to the dark side, though Plagueis's attempts to create life did inadvertently cause Anakin's conception.
In canon it was Kirak Infil'a , Cere Junda, Obi-Wan and Lord Momin . All messed him up quite badly with Kirak winning round 1 but losing round 2 and Momin cutting off his arm. Obi-Wan actually beat Vader. In Legends it was Shaa Koon, An'ya Kuro, a clone of Maul and Galen Marek.
Arguments might be made that he suffers from dysthymic disorder (mild but persistent and intrusive depression) because he does not openly demonstrate his suffering at the story's beginning, or posttraumatic stress disorder because these problems follow the traumatic events of Star Wars Episode III: Revenge of the Sith.
In a study published in the journal Psychiatry Research, French psychologists and psychiatrists determined that Darth Vader had six of the nine criteria used for a BPD diagnosis, as defined by the Diagnostic and Statistical Manual of Mental Disorders (DSM): Impulsivity. Rage and anger management issues.
It is widely speculated that Palpatine deliberately ensured the suit would be agonizing, keeping Vader angry, dependent, and subservient—turning pain into a tool of control.
The conflict between Anakin and Obi-Wan
Anakin's fear of losing Padme and being manipulated by Palpatine led him to make a choice, and he betrayed the Jedi Order. When Anakin confronts Obi-Wan on the planet Mustafar, his thoughts are clouded by the Dark Side.
Obi-Wan Kenobi (at peak, Mustafar era) - Already beat Vader at his prime (Anakin) once. Post-suit Vader is even slower and less versatile. Luke Skywalker (post-ROTJ Legends or Canon TLJ era) - Becomes one of the most powerful Jedi in history. By TLJ, he's surpassed Vader by a wide margin.
His brief joy at finally killing Obi-Wan instantly changed to shock and disbelief. Vader thought he knew everything Obi-Wan did, but clearly that was not the case.
As their lightsabers clash, Obi-Wan smiles serenely. He sees a future beyond the fight. It's a moment of sacrifice when he allows Vader to strike him down. But this act makes him immortal in the Force.
It kicks off right after the end scene of ROTS and shows Vader beginning his hunt for Jedi in his new body. His very first target is a Jedi Kirak Infil'a, a Jedi who lived for combat who nearly kills Vader.
Vader breaks free of the operating table and takes a few steps before doing the only thing anybody in his position could do, he screams an unholy, bloodcurdling scream. His vocal computer has nothing close to this sound in its database so it translates it to the infamous 'Noooooooooo'.
Darth Vader's failure to recognize Leia as his daughter in Star Wars: A New Hope stems from George Lucas's late decision to make Luke and Leia siblings. Leia's Force abilities and her lack of awareness of her true identity also contributed to Vader's inability to sense their familial connection.
In Star Wars lore, Order 37 was a grim Clone Trooper contingency plan to capture a wanted individual (often a Jedi) by taking a civilian population hostage, locking down the area, and threatening mass execution if the target wasn't surrendered, making it a horrific tactic used by the Empire to force Jedi compliance. It was considered more brutal than Order 66 because it targeted civilians directly, forcing Jedi to often turn themselves in to save innocent lives, as seen on planets like Bellassa.
Revenge of the Sith
Palpatine explains that Plagueis was so powerful and wise, he had mastered the dark side of the Force to such an extent that he could cheat death (mostly saving people he cared about from death) and create life; unnatural abilities which are unknown to the Jedi.