Palpatine's hatred of lightsabers actually explains both why he used one in the prequels, and mostly why he did not in Return of the Jedi. In broader Star Wars canon, it has been confirmed that Palpatine despises lightsabers, and sees them as a large contribution to the Jedi's dogmatic beliefs.
Palpatine's skills with a lightsaber and the dark side were rivaled by only a few, yet there were only a few instances in both continuities of him demonstrating his legendary lightsaber skills. Much of Palpatine's backstory was revealed in the Legends-era novel, Darth Plagueis.
Apparently, Sidious had no interest in the weapon because he left it behind when he took Maul captive. Mandalorian Prime Minister Almec, who orchestrated his escape from prison, informed the powerful Sith that some of his followers had recovered the Darksaber.
Palpatine understood the history of the galaxy as a constant war between the dark side and the light, embodied by the Sith and the Jedi. He sought to bring about the ultimate triumph of the Sith, extinguishing all trace of the light.
Qui-Gon is one of the most powerful Jedi in the saga: highly skilled in the Force and mastering abilities that other Jedi couldn't, including the ability to consciously manifest after death. But more than his abilities as an individual, it was his maverick philosophy that the Emperor feared.
Years after his death, during her duel with Jacen Solo, Lumiya alluded to Palpatine, saying he was a "psychopath consumed by power.". Palpatine's manipulative behaviour cannot be exaggerated as he manipulated the entire galaxy into doing his bidding.
Yoda struck the Podium too hard to control his landing, and he rolled off the main portion to the edge where he desperately attempted to climb back up. His hold on the smooth edge failing, Yoda lost his grip and fell several stories to the floor. Yoda chose to retreat as Sidious cackled in triumph above him.
Sidious himself felt that he and his peers had outgrown the use of lightsabers, and only continued carrying them to mock the Jedi. He ultimately viewed his own lightsabers as little more than an affectation, and rarely wielded them in combat.
The novel explained that, had Vader killed Obi-Wan on Mustafar, he would have tried to kill Palpatine too, but given how badly wounded he was after the duel, his power wasn't the same and he was weak, both physically and mentally.
Because the Darksaber's sentience intertwined its fate with the rulers of Mandalore, Mando's rejection of that role meant that their wills could never align. That's why he has so much trouble wielding the weapon: it doesn't want to be wielded by a selfish bounty hunter who doesn't care about Mandalore.
The very first owner of the Darksaber was the man who created it, Tarre Vizsla. Very little is canonically known about Tarre Vizsla, other than the fact he lived during the Old Republic era and was, at that time, the only Mandalorian to have ever been accepted as a Jedi.
Yoda saw his lightsaber as a weapon and a meditative tool, and vowed to never use it again as an act of penance for his involvement in the Clone Wars. Yoda chose to teach Luke Skywalker to be a true Jedi Knight without relying on combat, emphasizing the importance of selflessness over fighting.
As well as being a gifted bladesman Sidious' connection to the Dark Side is extremely powerful, granting Sidious the ability to conduct force lightning. Likewise, Sidious took on both Darth Maul and Darth Vader as his apprentice, two of the most powerful Sith and best villains in all of Star Wars.
Well, first I will go over why he spared them. After Order 66, there were still a number of surviving Jedi. And while Palpatine knew that Vader was perfectly able to kill any remaining Jedi, there were too many for one man to kill alone. So, instead of killing all the Jedi he found, some were captured and tortured.
Summary. Palpatine's true source of power comes from his intense hatred for everyone in the galaxy, which only fuels his strength. Not only that, but the more people hate Palpatine, the stronger he becomes as well, making inspiring hatred a crucial part of increasing his strength.
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.
Yoda's presence on Dagobah was likely hidden due to his mastery of Force Stealth and the planet's connection to the Force. Yoda, with his enhanced Force abilities and potential home-field advantage, would have had the upper hand against Darth Vader if they engaged in a lightsaber duel.
Palpatine, known also by his Sith name Darth Sidious or simply as The Emperor, was a Force-sensitive Human male who served as the last Supreme Chancellor of the Galactic Republic, holding the position from 32 BBY until 19 BBY, and was the first Emperor of the Galactic Empire from 19 BBY until his death in 4 ABY.
Most viewers have forgotten that Palpatine seems to have been afraid of Yoda in Star Wars: Episode III - Revenge of the Sith - and even tried to flee from their duel. Yoda and Obi-Wan Kenobi were among the few Jedi to survive Order 66.
Palpatine chose to keep his face as a symbol of the Jedi's treachery and as a way to appear weak to his enemies. The Sith Lord's rise to power based itself on appearing weaker than he actually was, and he continued that until his death.
