An in-universe reason for choosing Dagobah is the planet's connection to the dark side. Force-sensitive beings can feel each other's presence through the Force. Since Yoda's is such a light in the darkness, he neesd to hide in the darkest of places. Dagobah contains a dark side nexus.
Yoda lived the planet Dagobah for the rest of his life. After his failure to defeat the Sith Lord Darth Sidious following the formation of the Galactic Empire, Yoda exiled himself to Dagobah. Using an E3-standard starship lifeboat, began his exile where he continued his studies of the Force.
Yoda realized that the Jedi's teachings had become outdated and a new generation of Jedi could learn from his mistakes. Yoda's exile was a form of redemption, allowing him to reflect on his failures and ultimately train Luke Skywalker contribute to the restoration of balance in the galaxy.
Qui-Gon explained that he had been tasked with guiding Yoda along this new path, teaching him to retain his consciousness after death and commune with the living. After Order 66 and the declaration of the First Galactic Empire, Yoda returned to Dagobah, living simply amid its many creatures.
Yoda chose not to train Luke in lightsaber combat to teach him that being a hero and aggressive warrior are not the core values of a Jedi. Luke Skywalker's actions in The Last Jedi show that he took Yoda's lesson to heart by prioritizing the use of the Force over focusing heavily on lightsaber training.
With Yoda's presence in the Force cloaked, there really wasn't any way for the Empire, Darth Vader, or Vader's Inquisitors to find the Jedi master. Another potential explanation is the planet Dagobah itself.
So, it's likely Yoda didn't want to interfere and alter the future, as he'd be at risk of preventing the Sith from being defeated many years later. While Yoda sensed that the Sith's plan involved the Clones, it was too late to prevent Order 66.
Yoda was not only weakened physically, but mentally and emotionally he was reeling from Order 66 and the deaths of so many Jedi. He may have had the light side of the Force with him, but at this moment it was no match for the dark side.
Yoda had to shoulder that decision for years. However, he ultimately understood the importance of life, and the power he could have used to defeat Dooku would have been much better used to preserve two lives. Over the years, Dooku would commit countless atrocities and also suffer incredibly embarrassing defeats.
Aside from agility and telekinesis, Yoda could absorb and redirect Force attacks, like lightning. Because of his higher understanding, he would easily overcome Darth Vader in a fight, though that doesn't mean it wouldn't be a difficult battle.
A duel took place in the Cave of Evil between Luke Skywalker and a vision of Darth Vader. It was part of Skywalker's Jedi training by Yoda because if he entered the cave, he could face his darkest fears.
Dagobah was one of the purest planets in the galaxy, alive with the Force thanks to its abundant life. One cave in the planet's swamps roiled with the dark side. During the Clone Wars, the spirit of Qui-Gon Jinn led Yoda to this cave, where Yoda had a vision of Darth Sidious's triumph over the Jedi.
Since the planet Dagobah has strong ties to the Force, it makes sense that Luke gets a strangely familiar feeling while there that he can't quite place. Yoda tells him that through the Force he can see the past, which is likely why he gets a sense of déjà vu when on the planet.
The emperor of evil is in close proximity to the Jedi, and not just any Jedi. Some incredibly powerful Jedi like Yoda, Mace Windu, and Obi-Wan Kenobi failed to realize what he was. For whatever reason, none of these Jedi could sense that Palpatine was the Sith Lord they'd be searching for.
All the official Star Wars merch calls him The Child. On the show, they call him The Asset. What gives? The short answer is that “Yoda” is the name of a character, not a species, and the character we see on The Mandalorian is different from the Yoda we know and love from the Star Wars movies.
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.
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.
The base assumption of why Obi-Wan doesn't remember R2-D2 -- in light of the prequels -- is that Obi-Wan is feigning ignorance in A New Hope to downplay the importance of the droid's arrival. That explanation holds the most water for a number of reasons.
If Obi-Wan had admitted that he knew R2-D2 and that R2-D2 had belonged to Anakin, Luke may have started asking both of them more questions about his father. To prevent Luke from finding out the full truth before he was ready, Obi-Wan decided to tell more half-truths and pretend he had not known R2-D2 for years.
Star Wars Explained - A long time ago, in a galaxy far, far, away... Why didn't Yoda train Anakin Skywalker if he really thought that he was "the chosen one"? Yoda didn't want Anakin trained. He considered him to be dangerous, full of fear which could potentially be catastrophic.
Instead of teaching Luke with his lightsaber, Yoda challenges him in other ways—showing that Luke doesn't need to be a great warrior to be a true Jedi Knight. It's a lesson Yoda and the rest of the Jedi Order learned too late, but was one that was vitally passed on so Luke could rebuild the Jedi Order.
