There is no evidence that Obi-Wan and Padme had an affair, and it is highly unlikely given their close relationship. They were friends from childhood, and they had a deep mutual respect for each other. Any speculation about an affair between them is nothing more than fan fiction.
Many fans of the franchise theorize that Padme Amidala – Anakin's love interest and actual wife – has cheated on him. The theories claim that she had an affair with either Clovis or Obi-wan Kenobi. Both theories are not true.
This fell in line with various fan theories and non-canon novelizations that suggested Obi-Wan and Padmé had an affair sometime during the Clone Wars. In the Star Wars prequel movies, Obi-Wan often has a duty to protect Padmé, but there was never any sense of romantic feelings.
Short answer: no. Her little run-through with Clovis was during her early Senatorial days, before Anakin came along and fell head-over-heels in love with her. Any feelings she exhibited for the former on Scipio were purely out of respect or for business (since he was a powerful member of the Banking Clan).
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.
Did Anakin still love Padmé as Darth Vader? Even as a Sith Lord, Anakin still loved Padmé very much, but felt great guilt for his actions against her.
In Episode III, just before they are to set off on their respective missions, Obi-Wan and Anakin share a farewell. Anakin admits to Obi-Wan that he has been arrogant and unappreciative of his training, and apologizes to his master.
He knows it's Anakin, and the events in this week's episode of The Clone Wars, "A Distant Echo," prove it. And I think Padmé is savvy enough of a political operator to let people think that Clovis could have been the person who fathered the child, if only to avert suspicion from her relationship with Anakin.
However, when they next met in Star Wars: Episode II – Attack of the Clones, Anakin and Padmé's feelings for one another grew into something resembling love, and their wedding at the end of the film solidified their relationship as one of the most important romances in Star Wars history.
The film doesn't flinch away from how horrific that act is, especially as it begins the downward spiral of Padme's death. Nonetheless, as she dies, Padme tells Obi-Wan that there is still good in Anakin. Even something as heinous as that couldn't fully break her love for Anakin.
At some point after his transformation into the armored Darth Vader, Amidala's husband, the fallen Jedi Knight Anakin Skywalker came to visit the mausoleum, stricken by grief and remorse for his part in her death.
Order 66 was executed in 32 BBY, so Obi-Wan was twenty-five when he dueled his former pupil on Mustafar, saw Padmé die of hEaRtBrEaK—I'm sorry, but that motivation still enrages me after all these years—and made sure that Luke was delivered safely into the arms of his Skywalker uncle and aunt on Tatooine.
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.
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.
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.
If you are asking about Vader post-Mustafar, then no, she doesn't. Padmé doesn't seem to know Obi-wan cut off his limbs and left him to burn alive, Obi-wan didn't believe Anakin to be alive and Anakin's surgeries were still happening as Padmé died so there was no way for her to know.
Senator Padmé Amidala of the planet Naboo became pregnant during the Clone Wars with her husband, Jedi Knight Anakin Skywalker, as the father. She gave birth to twins, Luke Skywalker and Leia Organa.
To hide the birth of her twins from both Darth Vader and more importantly Palpatine. The fact that Amidala had given birth to twins was a secret known only to a few after her death. The mortician Commodex Tahn used a hologram to make her still appear pregnant during her funeral.
In Legends, Luke and Leia do eventually discover their mother's identity during the Swarm War Trilogy.
Padmé died shortly after giving birth to Luke and Leia, swearing with her last words that there was still good in Anakin Skywalker. The twins were split up, with Luke going to Tatooine with Obi-Wan while Bail took Leia to Alderaan.
Anakin Skywalker never knew Padmé was pregnant with twins, and he believed his child had died with his wife. He had no idea Padmé had given birth before she died, still less that the Jedi had spirited the children away and hidden them.
Anakin Skywalker
He is the secret husband of Padmé Amidala, the father of Luke Skywalker and Leia Organa, the father-in-law of Han Solo, and the maternal grandfather of Ben Solo.
It is unclear whether Yoda would be more or less forgiving than Obi-Wan but one thing is certain - the former Grand Master would be ready to treat Anakin as an ally, following the events on the second Death Star. In Star Wars: Revenge of the Sith (2005), Yoda never really lost faith in Anakin in the way Obi-Wan did.
In the material around the film from the Legends timeline, it's established that by the end of Star Wars: Episode III - Revenge of the Sith, Kenobi was one of the characters who knew Anakin's Sith name was Darth Vader. However, what he didn't know was that he was still alive after Mustafar.