Palpatine did know of Anakin's marriage to Padme, her pregnancy and Luke and quite possibly, Leia.
- Palpatine was the one who brought Anakin and Padme Together.
Anakin never told Palpatine of his marriage to Padme but Palpatine knew. How did he come across this information? Well, because he was the one who played matchmaker between them behind the scenes. The second film explains that Anakin has harbored feelings for Padme since he was a little boy in The Phantom Menace and Anakin didn't do a good job of hiding it. Attack of the Clones also shows that Palpatine and Anakin are good friends. I'm sure Anakin brought up the subject of his crush with Palpatine and Palpatine knew of his feelings for Padme. Padme was almost killed twice in the second film: at the landing platform and almost in her Crouscant apartment. Both were carried out by Zam Wessell but under the orders of Palpatine under the names of Jango Fett and Count Dooku. After the attempt on her life, Padme chats with the Jedi and Palpatine in the Chancellor's office at the beginning of the film. Palpatine suggests that Obi-Wan protect her because the "thought of losing her is unbearable." Knowing Obi-Wan's padawan was Anakin, it would force the two together. The second attempt was used to let Anakin be alone with Padme. It would only be a matter of time before something formed out of it (and we know, it did). When Palpatine reveals himself to be a Sith Lord to Anakin in Episode III, he says "Join me and you'll be able to save your wife from certain death" and Anakin's reaction is total shock ("What did you say?") This leads to the fact that Anakin did not tell Palpatine his secret nor of his nightmares. Palpatine knew of his wife because he was the one who brought them together, knowing she was Anakin's ultimate downfall. Since Anakin was The Chosen One who was to kill the Sith, Palpatine decided to turn his threat into his ally and used the person he loved most of all to bring him to the Dark Side (aka Padme).
- Palpatine created Anakin's nightmares of Padme dying
Palpatine knew of Anakin's marriage to Padme and of Anakin's fear of losing those he loved to death. In the beginning scenes of Episode III: Revenge of the Sith, Palpatine reminds Anakin of "what he told him of his mother and the sandpeople." Palpatine was the only one Anakin told about this, besides Padme. Palpatine somehow knew of Padme's pregnancy (how the information was uncovered is unknown to us, the audience), however it is strongly implied that Palpatine is the source of the "visions." He brings up the matter of Plageuis being able to save those he loves the most from death. He knows death is Anakin's biggest fear. He implied the apprentice to be himself to Anakin but this is false as he later tells the newly-turned Vader later on in the film, "To cheat death to the power of only one has achieved but if we work together, I know we can discover the secret" This means he was lying to Anakin before when he said the Plageuis taught his apprentice "everything" he knew. It was a rouse to catch Anakin's interest, not to be taken as whole truth. The second imply was when he revealed himself as Darth Sidious to Anakin and he stated "Join the dark side of the force and you'll be able to save your wife from certain death." Anakin is shocked by the statement ("What did you say?") because he never told Palpatine of his nightmares nor that is was Padme who was dying in the dream. The only ones who knew was Padme and Yoda (though he didn't know Padme was the person dying). Anakin kept this oddly, to himself. This means that Palpatine had to have created the dreams to have known who was dying in the dream and her dying in childbirth means he knew of the pregnancy.
- Palpatine killed Padme during Anakin's suit construction
This goes with the fan-theory that Sidious killed Padme and that she didn't die of a broken heart. I have to agree with this. There is evidence for this if you look deeper in the film storyline and plot. You know that Padme is quite alive after her encounter with Anakin on Mustafar and that the droids can't explain why she is dying but can only guess that she "lost the will to live." Padme is the only one who mentions that her heart is "breaking," so we assume she died of a broken heart as no one mentions her cause of death. Anakin sensed her during his operation and asks Sidious how she is. Sidious knows that she is dead. And how did he know that she died? The dream was that she died in childbirth, not of a broken heart. Throughout the visions, Padme is screaming for Anakin to "help her" and for some reason, she can't "hold on." This can mean that she felt Anakin and Anakin felt her throughout the entire process. When her life force vanished, Anakin sensed this and questioned what happened to his wife, "Where is Padme? Is she safe?" and later remarks, "She was alive! I felt it!" Hence, why she tells Obi-Wan there is "still good in him," and seems to struggle to hold on to consciousness. If this theory is true, Sidious would have sensed her giving birth. And of Vader? Did he sense something too? We'll get to that later. This theory makes sense, though. Sidious used this as the final breaking point to turn Anakin fully into Vader (hence his grinning when Anakin mourns Padme's death) and lies to him by telling him that he "killed" his wife.
- Palpatine tells Vader of his son's existence, how did he know of Luke? Where did he get this information?
Alrighty, so we get to the next point of how the Emperor knew of Luke. In The Empire Strikes Back, Vader learns he has a son from the Emperor ("I have no doubt that this boy is the offspring of Anakin Skywalker"). How did Palpatine come across this information? Where did he learn this? It is not stated. Palpatine knew of Padme's pregnancy and if he killed her, would have sensed her in childbirth. In fact, we actually know the Emperor has sensed Luke before! In Return of the Jedi, Vader tells the Emperor that Luke is on Endor and that he sensed him there and the Emperor replies with, "Funny how I have not sensed him." This would make sense if the Emperor killed Padme and sensed the children but could not locate them. When Luke arrives on the picture, Palpatine could be able to figure out that he sensed this boy before and could piece together that the boy named Luke Skywalker was the same baby he sensed at Padme's death. What about Anakin? He sensed Padme before during his operation ("She was alive! I felt it!"). After the Emperor states his fact of Luke being Anakin's son, Vader replies with, "How is that possible?" The Emperor answers, "Search your feelings Vader, you know it to be true." Hmmmmm.......
- Obi-Wan tells Luke that he and Leia were hidden for protection. But if nobody knew of the their births, why protection? Somebody had to of known about them.
When Luke finds out the truth of his parentage, he talks to Obi-Wan in Return of the Jedi and the subject of his twin sister is brought up. Obi-Wan tells Luke, "To protect you both from the Emperor, you were hidden from your father....The Emperor knew as I did that if Anakin had any offspring, They would be a threat to him..." The Emperor knew as Obi-Wan did? They hid the twins so that the Emperor and Vader could not find them, but it doesn't mean that they did not know of them. In the prequel trilogy, Yoda only states, "Hidden safe the children must be kept." But if the Emperor told Vader he killed his wife, it is possible that he could assume that he killed their child as well. Remember when he told Padme of his nightmare? She questioned what happened to their child, and he responded that he didn't know what happened to their baby. We can assume he sensed Luke, but not Leia.
- Palpatine may have known about Leia too.
Vader did not sense Leia's birth, this is made clear in the sixth episode. The Emperor never states of Leia or Vader having a daughter. Obi-Wan states in Return of the Jedi, "To protect you both from the Emperor, you were hidden from your father when you were born. The Emperor knew as well as I that if Anakin had any offspring, they would a threat to him, that is the reason why your sister remains safely anonymous." This could mean that Vader might not have sensed a connection between himself and Leia but Palpatine might have. He chose to keep quiet about it because she would have been a threat to Vader. Palpatine never mentions Luke for a good while between the fourth and fifth films. It is possible that Leia's heritage may not have been a secret after all....Vader did not know the fate of his child in his dream and this most likely was what happened in real life. He may have sensed Luke, but not Leia.