Arguably, most Star Wars plot points revolve around characters simply not knowing something, very often about their family history. But, on top of all of that, the biggest reason Obi-Wan doesn't know Anakin is alive is that the last time he saw Anakin Skywalker in Revenge of the Sith, Ben literally left him for dead.
Anakin needed to be killed to keep him from turning into a galactic dictator. But Obi-Wan couldn't bring himself to kill someone he considered a brother. As Anakin jumped off the floating platform, his intentions were evil-- he was looking to cut Obi-Wan in half the way Kenobi himself had once done to Darth Maul.
During their encounter, the Third Sister shocks Obi-Wan when she tells him that Anakin is alive. From his reaction, it is clear that this is the very first time he heard that Anakin is alive. This means he went about 10 years believing that Anakin was dead, only to find out he was alive all along.
First and foremost, Obi-Wan didn't want to have to confront and try to kill Anakin, we see this all the way until their final conflict in their duel where Obi-Wan pleads with Anakin to not make him do what he knows he'll have to do if Anakin tries to attack from the low-ground.
Anakin admits to Obi-Wan that he has been arrogant and unappreciative of his training, and apologizes to his master. Obi-Wan assures Anakin that he is proud of him, telling him that he has become a "far greater Jedi than I could ever hope to be."
He slays Sidious and returns to Obi-Wan, begging for atonement by execution, only to be met with true forgiveness instead. But just as this fantasy Obi-Wan refuses to strike his former friend down, Vader refuses to turn his back on the dark.
We go for the more simple answer, further considering the details of the question itself. If Anakin didn't go into that chamber as the Jedi confronted Palpatine, then Mace Windu would have defeated Palpatine, killing him. If you remember, Mace had him. He was ready to kill him.
Obi-Wan knew it was only a matter of time. So, he made the difficult decision to use his learnings and become one with the force, rather than let Vader decapitate him.
Yes he did. And the saddest thing is that there was nothing he could do about it. He was broken. The first case is shortly after ROTS when Vader was making his Sith lightsaber.
Before he discovered Vader had survived Mustafar, Obi-wan lived with the regret of killing his son, brother and best friend. After, he regretted not killing him and wondered if he had only made things worse by pushing Anakin further into dark side and Palpatine's arms.
No. Her dying words were there is still good in him. Obi-Wan didn't tell her what happened after she lost consciousness on Mustafar.
Only a Master of Evil
The last time Obi-Wan saw Anakin Skywalker was the fateful duel in which he chopped his apprentice into bits and left him melting on the side of a volcano.
Though there was some debate among the fans that Anakin Skywalker's son, Luke Skywalker, was actually the Chosen One since he caused his father to destroy Darth Sidious, the debate was settled when George Lucas himself confirmed in an interview that Anakin, even after becoming Darth Vader, was still officially the ...
When Palpatine reveals himself as a Sith Lord to Anakin in Revenge of the Sith, a small detail shows that he considered dueling Anakin. A small detail in Star Wars: Episode III – Revenge of the Sith suggests that Palpatine toyed with the idea of killing Anakin—before he had fully seduced him to the dark side.
In the annals of Star Wars history, many believe Obi-Wan Kenobi was the key to saving Anakin Skywalker's soul before his fall as Darth Vader. However, as Kenobi's recent Disney+ series showed, that was never really the case. Anakin lost himself to the Dark Side way before Obi-Wan's intervention.
He couldn't bring himself to kill Darth Vader, however, because he continues to associate him with the Anakin he trained as a boy. This is also the exact reason why Obi-Wan didn't kill Anakin on Mustafar despite the opportunity a decade earlier in Star Wars: Episode III - Revenge of the Sith.
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.
Most specifically though, Vader hated the most important person in his life, his son Luke Skywalker. Vader believed that Luke was the only thing standing between him and ultimate power. So, in short, the person Darth Vader hated the most was his own son- Luke Skywalker.
Darth Vader showed no emotion at all when he killed Obi-Wan Kenobi. If you watch the scene carefully, you will see Kenobi pausing. He was letting Vader kill him. Whether Vader knew this at the time, or discovered it later, is an open question.
For years, Vader hated Obi-Wan, having been struck down by his mentor and left for dead while also believing the Jedi had worked to turn his true love Padmé against him.
If Anakin had never fell in love with Padmé, he would've never turned to the Dark Side because it was his fear for losing Padmé and his two unborn children which caused him to be easily seduced by the Dark Side of the Force. It was his fear which made it much easier for Palpatine to manipulate Anakin.
Did Padme ever cheat on Anakin? No. As explained above, Padme did not cheat on Anakin with either Obi-Wan Kenobi or Rush Clovis.
One of the main reasons why Yoda would've won against Anakin is simply because he was far better trained than him. Yoda could see the moves his opponents were going to make before they made them; therefore, battling against Anakin would've put him at a far heavier advantage.