Darth Vader acts like he doesn't even know C-3PO or R2D2. They were with him since he was a child. He did everything he could to forget his past. Also, his plating had been replaced many times, and protocol droids all look very similar.
Obi-wan responds to starwars.wikia.com/wiki/Luke_Skywalker saying R2 belongs to him with, “I don't seem to remember ever owning a droid,” which is technically true, because Obi-Wan never did “own” R2 or C-3PO. Obi-Wan then makes a comment that suggests he's more than aware of R2's impressive capabilities.
C-3P0's memory was wiped at the end of Episode III so if he wasn't told he had no idea that his maker was the future Darth Vader. R2-D2 remembers it all and if I had to guess he is quiet sad about Anakin's turn to the dark side.
Vader himself saves Threepio from destruction in the final pages of Marvel's Star Wars, before the series gets a relaunch taking place after Empire Strikes Back.
Darth Vader acts like he doesn't even know C-3PO or R2D2. They were with him since he was a child. He did everything he could to forget his past. Also, his plating had been replaced many times, and protocol droids all look very similar.
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.
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.
Leia's Force abilities and her lack of awareness of her true identity also contributed to Vader's inability to sense their familial connection. Vader's denial of Anakin Skywalker's legacy and his fear of getting hurt again prevented him from realizing the truth about his children until later in the original trilogy.
Either way, while Vader can use most other Force abilities, Force Lightning needs to be channeled, and Vader's limbs are explicitly not connected to the Force. The Star Wars: Episode III - Revenge of the Sith Visual Dictionary confirms Darth Vader cannot use Force Lightning, and even suggests this is the reason why.
The sequence calls back to a similar scene in Revenge of the Sith, when Bail Organa orders Threepio's memory be erased to prevent him from sharing information about Anakin Skywalker's fall to the dark side.
She senses Anakin when she reaches out to the pilot — and Vader realizes that Ahsoka, his former Padawan, lives on. In Season 2, Episode 18, “Shroud of Darkness,” Ahsoka's guilt manifests as a vision of Anakin, who's angry with her for leaving him all those years ago.
Master Yoda knew that Darth Vader was once Anakin Skywalker - the boy he sensed too much fear in to train way back in Star Wars: Episode I - The Phantom Menace.
Does KYLO Ren know Darth Vader is his grandfather?
Kylo Ren was always obsessed with his grandfather. He didn't learn he was the grandson of Darth Vader until he was a teenager, when a recording from Bail Organa - intended to be a private message for Leia - was shared with the entire galaxy.
Since Obi-Wan and Anakin often fought together, Obi-Wan was friends with R2-D2 as well. This means that although R2-D2 might not have immediately recognized Obi-Wan on Tatooine due to his age, Obi-Wan should have recognized the droid.
After decades of missions with R2-D2, Luke Skywalker was reasonably fluent in droidspeak. The most common way for binary droids to communicate with organics was by writing, conveyed via another computer system. This is how astromech droid copilots would speak with the pilot of a starfighter.
secondly, in Legends, R2 was given programming that actually restricted him. from sharing any information with Luke or Leia. about their parents or relation to one another. this was all part of the plan. to conceal this information from the twins.
After the Clone Wars, however, Brooks Propulsion Devices, the company responsible for the development of his boosters, was shut down, and his rocket boosters were eventually damaged and thus could not be repaired. Despite this, however, R2 hardly regretted the loss of his ability to fly.
