Vader didn't sense Luke as someone special until he made the connection that Luke was his son. Before that he was just another person with a connection to the Force. So Vader could sense Leia as much as anyone else but since he didn't know about his paternal question to her she didn't stand out to him as unique.
Leia was not using the Force or was currently Force-sensitive during her confrontation with Vader. She began training as a Jedi years later. All these reasons prove my point: Vader didn't know Leia was his daughter, and felt no presence of the Force in her, as she was not currently strong with the Force.
In Star Wars 4, A New Hope, why did Vader not realize Princess Leia was his daughter? Because she had not yet had the Force awakened in herself. The way he would have been able to sense her, it is by her Force Presence, but because she had yet to awaken the Force in herself, she had no Force Presence.
Before she became a Jedi hunter, she had possession of a droid. However, it was taken away from her, like many of her past belongings and acquaintances. During her time as an Inquisitor, the Third Sister wore black armor with a cape, and wielded a red-bladed Inquisitor lightsaber.
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.
As soon as Anakin Skywalker became Darth Vader, he already faced his most persistent nemesis and lost, namely his own master, Obi-Wan Kenobi.
Although C-3PO is a tell-all, it's possible that he was directly programmed not to say who Leia is. This is something that George Lucas himself suggested in an interview back in the 1970s, which made it into the book The Making of Star Wars: The Definitive Story Behind the Original Film.
As the theory explains, Wookiee culture dictates that when Wookiees lose a loved one, they are not supposed to touch anyone until they have had time to grieve in private. This explains Chewbacca's actions.
Theory 1: Leia Doesn't Remember Ben Is Obi-Wan
Throughout her encounters with Kenobi in the series, he refers to himself as Ben. The most straightforward explanation would be that Leia knows the person who rescued her is Ben, and never connected the dots that Ben is actually Obi-Wan.
However, because he saw their dynamic as a source of weakness, he opted to spare them. Now that the Empire had gained the upper hand against the rebels, their survival didn't mean much to him in the grand scope of the galactic conflict at hand.
Obi-Wan greets R2-D2 and later recalls “not owning a droid.” Obi-Wan purposely withheld information from Luke in order to keep Luke from straying away. This could offer an explanation as to why he appears to not know who R2-D2 is. Further in Empire Strikes Back, neither Yoda nor Darth Vader recognizes either droid.
Obi-Wan never said that he didn't recognize the droids, but even if he did, he's been known to fib before. For instance, he initially lied to Luke about Anakin's fate (well, I suppose it was true from "a certain point of view"), and in a sense, he's been lying for years under his fabricated identity of Ben Kenobi.
She also knows Obi-Wan, and she knows him well. Her holographic plea for help, already iconic, will never be the same. She knows Obi-Wan's real name as well as his alias of “Ben.” When Luke comes barging into her cell and says, “I'm here with Ben Kenobi,” Leia jumps off the bunk in an instant.
This information comes to light form the comic series Darth Vader: Dark Lord of the Sith by Charles Soule and Giuseppe Camuncoli, in particular issue #7. Palpatine admits to Darth Vader that the Jedi he actually feared most was none other than Jocasta Nu.
“Carefully moving through the swamp while staying beneath the fog, Yoda soon spotted the boy and his droid unpacking their supplies. Even though the droid was caked with algae, dirt, and stomach fluid, its appearance and familiar blips were still quite recognizable. R2-D2.
However, R2-D2's memory is not wiped; as a result, R2-D2 is the only surviving character at the end of the saga who knows the entire story of the Skywalker family. Both R2-D2 and C-3PO end up in the possession of Captain Raymus Antilles (Rohan Nichol) onboard the Tantive IV.
Obi-Wan was one of the prominent generals of the Galactic Republic during the Clone Wars, who fought side by side with Anakin and the 501st. So, it could be likely that the Clone trooper indeed recognized the Obi-Wan.
The actual answer as to why doesn't Owen remember C-3PO is that it's a plot-hole in the saga, since George Lucas wrote A New Hope with little to no idea of where the droid's long and winding backstory would lead him.
That's right, Chewbacca and Obi-Wan have a history together, as they fought side by side in this conflict. In fact, with Obi-Wan's help, Chewbacca successfully colonized Alaris Prime and turned it into an economically prosperous stronghold for the Wookiees beyond their home planet of Kashyyyk.
This means Threepio would now remember the identity of Darth Vader, the events of the Star Wars prequels, and Luke and Leia being siblings. All decades too late, of course.
89-90). Thus Othellos actions directly lead to his downfall. In Revenge of the Sith, Anakin is also responsible for his own downfall. His pride and anger cause him to kill his superior and betray everything he has sworn to protect.
One of the most iconic lines in the entire franchise (and in movie history), is "May the Force be with you." But there are many more lines throughout the 130+ hours of Star Wars content, and these are some of the best, broken down by which movie or TV show they appear in.