Yes he learned shortly after the destruction of the Death Star I that Luke was his son, and after he attempt to capture him on cloud city he even reached out to him through the force confirming to Luke he was indeed his father.
How does Darth Vader find out that Luke is his son?
Vader was hunting down the pilot who blew up the Death Star, and hired Boba Fett to find them. Boba was unable to, but he did give Vader a name: “Skywalker.” This, combined with his knowing Luke was Force-sensitive and had been trained by Obi-Wan, was what made him realize the truth.
In the first two Star Wars films, Vader comes face to face with her multiple times and doesn't recognize her as his daughter. As for Luke, he knew from the moment he heard the name he had a son and tried to find him. When he fights Luke again in Return of the Jedi, Vader finally recognizes Leia as his daughter.
Does Darth Vader ever find out Leia is his daughter?
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.
Alderaan's princess knew she had been adopted by Bail and Breha Organa after the Clone Wars, but she had no idea who her parents were. That was until Luke Skywalker told her the truth - that he was the son of Darth Vader, and that she was his sister.
Vader finds out Luke is his son - Empire Strikes Back (1980)
Did Yoda know Luke was Anakin's son?
Returning to Dagobah to complete his training, an ailing Yoda told Luke the terrible truth that Vader was his father, Anakin Skywalker. Rather than destroy his father, Luke sought to bring him back into the light. At 900 years old, Yoda passed away, telling Luke that there was another Skywalker.
Darth Vader's obsession with Luke Skywalker in The Empire Strikes Back is seemingly due to the latter's destruction of the Death Star battle station, but his revelation to Luke and brief dialogue with Emperor Palpatine recontextualizes his pursuit.
With Anakin's mother dead, his padawan Ahsoka estranged and his faith in Obi-Wan and the rest of the Jedi council fading, Padmé was all he had left by the climax of Revenge of the Sith. By eliminating her, Palpatine would be the only one left for Anakin to turn to and therefore would have complete control over him.
At some point after his transformation into the armored Darth Vader, Amidala's husband, the fallen Jedi Knight Anakin Skywalker came to visit the mausoleum, stricken by grief and remorse for his part in her death.
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.
Did Anakin Skywalker/Darth Vader love Luke Skywalker? Yes he did. Now as someone consumed by the dark side, he really sucked at showing it at first. His idea of love was to turn his son to the dark side so they can rule the galaxy together.
Although the decision to turn to the Dark Side was Anakin's alone, the choice did not come from thin air. His natural prone to impulsivity and emotion without the support systems he needed in place made it easier for Anakin to stumble down a path of darkness.
R2-D2 was present when Padmé gave birth to Leia and Luke, so he knew Luke was Anakin's son – but what he didn't know was that Anakin became Darth Vader. In addition to that, Anakin's fall was surely a painful event in R2-D2's life, one that he definitely wouldn't like to remember or even talk about.
Over the next decade, the galaxy was on the verge of civil war with entire star systems—led by Count Dooku, Yoda's one-time Padawan—threatening to secede from the Republic by 22 BBY.
Din Djarin has been teaching Grogu how to navigate the galaxy, and Grogu could honor his father by becoming a bounty hunter in the future. Grogu does not have to be the new Mand'alor or a Jedi Master. Instead, Din Grogu could make his own through the galaxy, perhaps assisting the New Republic as a bounty hunter.
While he had suffered fatal injuries from the Emperor's lightning, Vader's redeeming final act restored his consciousness to Anakin Skywalker, and he had one last moment with Luke before peacefully accepting his death.
Shmi informs Qui-Gon that Anakin has no father, leading Qui-Gon to suggest that Anakin is a product of midi-chlorians (Force-imparting microorganisms). As the film progresses, Anakin leaves Tatooine to begin his Jedi training.
The final season of The Clone Wars reveals that freaking Darth Maul was aware that Anakin Skywalker would directly lead to the downfall fo the Jedi and the destruction of the Republic. Maul wasn't aware of these things because Palpatine slipped him a note, he, like other Force-users, saw into the future.
Vader presumedly wanted to give Luke the experience of pain during his attempt to get his son to join him, thereby making him more vulnerable to the dark side's power. For Vader, pain is his greatest tool and asset, as it ultimately gives him the power to wield the dark side of the Force.
However, when it comes to who Darth Vader hates more than anyone in the Star Wars galaxy, himself and Obi-Wan Kenobi don't hold a candle to the true point of Darth Vader's hatred, Emperor Palpatine.
tragically, he was not able to resurrect Padme. because she refused to go with him. due to his inability to let go, telling him she didn't know him anymore, jumping away from him to her death.
