Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence.
That was until Luke Skywalker told her the truth - that he was the son of Darth Vader, and that she was his sister. "It won't be easy for you to hear it, but you must," Luke told Leia before he revealed his secrets to her.
In short, yes. Darth Vader found out that Luke had a twin sister a few moments before his death. Leia also found out that Vader was her father when Luke told her on the bridge in the Ewok village.
Why didn't Darth Vader recognise Leia as his daughter in Star Wars: Episode IV? He didn't recognize her because he didn't know his daughter was alive, and he couldn't tell it from reading her mind because she wasn't aware of it herself.
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.
During the iconic opening moments of Star Wars: A New Hope, Darth Vader has a tense confrontation with Princess Leia, an adversary who, unknown to him, is actually his daughter. Despite participating in Leia's interrogation, the Sith Lord doesn't uncover his familial connection with the rebellious royal.
Luke, Leia, and Han are on Endor. First, Luke tells her Vader is his father. Her first reaction is one of slight revulsion, perhaps even of him. She gets a very concerned look on her face.
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.
However, she chose not to tell Anakin, presumably because he was about to go into a battle. Anakin was prone to letting his emotions affect him, and knowing that Padme was pregnant would've thrown him completely off the task. And Padme probably didn't think that her husband would be fighting battles for months to come.
This is not because the Third Sister knows that Leia is Anakin Skywalker's child; it is because the Third Sister found a link between Obi-Wan and Bail Organa and she believed Obi-Wan would do anything to save Bail's daughter.
In the post-2014 canon universe, the story that reveals Darth Vader discovering Luke Skywalker's identity (and thus the fact that the Death Star's destroyer is his son) is issue 6 of 2015's Star Wars comics by Marvel, which takes place sometime shortly after A New Hope.
did luke and leia ever figure out who their mother was? i only remember them talking about anakin :( Yes, they did. Eventually, Leia contact her good friend Pooja Naberrie to discuss her mother so they definitely knew about Padmé Amidala and the fact she was their biological mother.
Arguably, Vader loved Padmé even more than Anakin did. After what he did to Padmé on Mustafar, Vader was obviously devastated. The worst part was, he believed it was his own fault, even though the choking only had a very indirect influence on Padmé's death.
As Padmé grows more and more visibly pregnant, why did no one wonder who the father was? Rush Clovis is really the only possible answer. The timeline matches up pretty well, and their prior relationship was common knowledge.
The film doesn't flinch away from how horrific that act is, especially as it begins the downward spiral of Padme's death. Nonetheless, as she dies, Padme tells Obi-Wan that there is still good in Anakin. Even something as heinous as that couldn't fully break her love for Anakin.
The marriage, witnessed by the droids C-3PO and R2-D2, was kept secret due to Amidala's place as a prominent Senator in the Galactic Republic and because of Skywalker's membership in the Jedi Order; the Jedi Code prevented Jedi from falling in love and forming attachments such as marriage.
In Star Wars Legends Leia was visited by the force ghost of her father Anakin Skywalker, the man who used to be Darth Vader. It wasn't a pleasant meeting as Leia was unable to forgive him for the things he'd done no matter how hard he begged, and it was the only time she saw him.
Leia and Han had three children, and they named their youngest son Anakin after Anakin Skywalker, Leia's biological father. Since Luke was the twin to spend more time with Obi-Wan in the old canon, it made sense that he, not Leia, was the one to honor Obi-Wan when naming his child.
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.
He only senses Luke when he actually using the Force, Leia is not actively aware or using the Force and therefore he does not sense her. He is also not looking for a daughter either until Luke spills the psychic beans on her later on.
As Leia is the daughter of a senator, constantly kidnapping her would inevitably lead to the Empire's connection to the kidnappings, which would cause unrest within the Senate, which Emperor Palpatine needs in order to keep his power at this point in time.
That's all you get. It's well known that Star Wars lead characters Luke Skywalker and Princess (now General) Leia are brother and sister. The estranged siblings didn't know about their familial relationship until "Return of the Jedi." They even shared a passionate kiss in the previous movie, "The Empire Strikes Back."