In the Star Wars movies, Darth Vader doesn't explicitly acknowledge R2-D2 or C-3PO as his old droids, but it's implied he might have recognized C-3PO in The Empire Strikes Back, as he stops Boba Fett from shooting the droid on Chewbacca's back, a nod to their shared past. Canon comics and extended universe stories confirm Vader did recognize them and was deeply disturbed by seeing them, but the films (especially during the original trilogy's production) downplayed this for narrative reasons, as the prequels hadn't established Anakin as their creator yet. Reddit +3
C3PO had his memory wiped at the end of the PT so he didn't remember who Anakin was. R2D2 did know who Anakin was, but he didn't know that Anakin ever became Darth Vader.
C-3PO had his memories wiped after Episode III, but R2-D2 did not.
Yes, he remembers everything about his past (just not based on reality), but he probably doesn't spend a lot of time thinking about it, and when he does, his memory of things is clouded and twisted by the lies of the sith, the dark side, and his own flawed thinking and character.
As can be seen in the movies, c3po is not the only protocol droid and they look very similar. Same with R2D2 he isn't the only blue astromech droid. The droids and galaxy all believe Anakin is dead. So there is no reason for the droids to know vader and no reason for Vader to recognize the droids.
Absolutely. Growing up on Tatooine, Anakin Skywalker was already accustomed to grasping and understanding many different languages. Not to mention, he was a droid fanatic himself—being a great mechanic—and most likely knew the language of Artoo's “droid language” or picked up on it quite quickly.
Because R2 and Yoda rarely crossed paths. At most R2 would remember Yoda but only as a Jedi master. To Yoda, on the other hand, R2 probably was a background droid.
After Anakin's fall and defeat, R2 left Mustafar with Obi wan and Padme. Once Padme died, Bail Organa took R2 and gave him to Captain Antilles on the Tantive IV. From there he became Luke's and then Leia's. Anakin and Padme traded droids as if they were wedding rings.
After Cad Bane had kidnapped and ransacked the memory of C-3PO and R2-D2 for information on the Senate Building's layout, he only had the incident wiped from their memories to avoid having any suspicion falling on him.
No, Darth Plagueis is not Anakin Skywalker's father; Anakin had no biological father, being born of the Force itself in response to Plagueis's dark side manipulations, with Palpatine's tales of Plagueis's power over life being a manipulation to turn Anakin to the dark side, though Plagueis's attempts to create life did inadvertently cause Anakin's conception.
Fun fact: Thrawn met Anakin on Battu during the clone wars, years later Thrawn and Vader went on a mission to Battu and just from observing Vader and seeing how he fought, felt, thought, everything. He found out that Vader was Anakin but kept the secret to himself.
While Star Wars has finally brought Luke Skywalker and Ahsoka Tano together in The Book of Boba Fett, it's not the first time the two characters have met.
Anakin reunites with C-3PO only after tragedy strikes and he returns to Tatooine too late to find his mother kidnapped and killed by Tusken Raiders.
It's because C3PO annoys him. He's always telling Han what he should do, or what the odds are. Han didn't like to be told what to do. Even Leia tells C3PO to shut up.
After Anakin falls to the dark side of the Force and becomes Darth Vader, he takes R2-D2 with him when he goes to assassinate the Separatist council, but he tells him to stay with the ship.