It's strongly implied in “The Rise of Clovis” episode of The Clone Wars show that Obi-Wan is aware of Anakin's relationship with Padmé, or at least his feelings for her. The Obsession comic basically confirms he knows, too.
Obi-Wan likely loved Padmé, but as a friend, not a potential lover. Obi-Wan Kenobi has brought up the questions of Obi-Wan's feelings toward Padmé again, but there's still no confirmation of anything romantic.
They may not know the extent of Anakin's relationship with Padmé, or even that they are legally married, but it seems abundantly clear that Yoda, at the very least, was aware of Anakin's strong attachment to Padmé, and that those feelings were reciprocated, too.
Yet some knew about their marriage, with Yoda likely being one of them. For the three years the Clone Wars waged, Anakin and Padme kept their marriage a secret from the Jedi Order. While their secrecy was impressive, there were still a few who caught on, especially those closest to Anakin.
Obi-Wan first met Padmé shortly after the Invasion of Naboo started, when he and his mentor, Qui-Gon Jinn rescued her from the Trade Federation's battle droids. They did not have much interaction with each other. However, throughout the Clone Wars, the two became close friends.
Obi-Wan couldn't help wishing Anakin the happiness he had been denied, and therefore, he decided to keep the marriage between Padmé and Anakin a secret. There is a tragic irony to this because, in truth, Obi-Wan shared Anakin's greatest weakness: attachment.
It is only then that Obi-Wan looks her in the eye and asks if the children she was carrying were Anakin's. She did not respond, but she did not need to, and at that moment he apologizes. It is unknown if he apologizes out of a sense of empathy or responsibility, but it should be the latter.
Every time she speaks, he remembers Padmé. Fighting alongside Sabé reminds him of fighting alongside his wife. While that is certainly painful enough, it's also reminds Vader of the man he used to be, a past he had long ago attempted to kill and bury. However, the memory of Padmé via Sabé won't let his past stay there.
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. For many years it's been assumed Master Yoda was aware from the day Vader gained his cybernetic enhancements and signature wheeze.
Anakin's vision did come true, as Padmé, heartbroken by her husband's downfall, loses her will to live and succumbs while giving birth to twins. Before her death, Padmé still believed there was still good left in Anakin and that one day he could be saved with the help of their children.
It's clear that Darth Vader wishes that Padmé joined him so that they could have remained together. But there are moments in Marvel's other Darth Vader series that suggest that, while the Sith Lord is very much still obsessed with the idea of Padmé, her betrayal may have caused him to think ill of his late wife.
Jedi Masters Obi-Wan Kenobi and Yoda watched Amidala's funeral from Senator Bail Organa's starship, the Sundered Heart. They didn't want to take the risk to come any closer and be found by the Empire, as they were certain that Emperor Palpatine's attention would be fixed on the funeral.
The dynamic between Anakin and Obi-Wan has always been one of two brothers who rarely got along. Though Obi-Wan was often an important ally for Anakin, the young Jedi could never see past his envy, even going far enough to allow himself to believe that his master was having an affair with his wife.
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.
Very few people knew that Darth Vader and Anakin Skywalker were the same person up to his death in 5 ABY. Imperials who knew in the current canon: Sidious (emperor), Grand Moff Tarkin, all or most of the Inquisitors, Grand Admiral Thrawn, various clones in the early empire.
At first, Ahsoka has no idea that Anakin Skywalker and Darth Vader are one and the same. She discovers the truth in Star Wars Rebels when she encounters the Sith Lord in a space battle. What she senses is so shocking to her that she passes out.
In the main Star Wars timeline, of course, Darth Vader's attempts to resurrect Padmé on Mustafar were doomed to failure. But it's fascinating to speculate what would have happened had he been successful. In that scenario, Padmé Amidala's return from the dead would not have provided the solace Darth Vader sought.
Anakin does not have even the slightest bit of remorse. By the end, he feels nothing but anger. Although he feels regret for killing Padme, he still helps the evil Emperor. The film ends with Anakins standing side by side with the man on whose behalf he has committed all his crimes.
She knew he was volatile and even murderous after he slaughtered the Tusken Raiders. As such, the only reasonable explanation for her marrying Anakin is that she was truly in love with him.
Obi-Wan spared Anakin despite knowing killing him would "burn his heart to ash" and feeling regret for what Anakin could have become. Obi-Wan's decision to spare Anakin was influenced by the dark feeling that accompanied Emperor Palpatine's arrival, preventing him from finishing him off.
