The Mandalorian method for forging beskar was a closely guarded secret, a skill passed on through generations to keep ancient armor intact and impervious. According to Mandalorians, all beskar belonged to them, but, over the course of history, many other parties claimed it.
What makes much of the armor in The Clone Wars different from Din Djarin's or Bo-Katan and her Nite Owl's is that it isn't pure Beskar. The Mandalorian makes a point of saying that he finds pure Beskar, which is the metal in its best and strongest state.
Mandalorian armor forged from beskar can withstand blaster bolts, nearly impenetrable protection that made the warrior class difficult to defeat at the height of their power.
Properties. Mandalorian iron, also known by its Mando'a name of beskar, was an extremely durable iron ore whose only known source was the Outer Rim world of Mandalore and its moon, Concordia.
In contrast, Din Djarin's armor was made from pure beskar, earned through the bounty on Grogu. This made Djarin's armor rare and even more durable than normal Mandalorian armor, allowing it to stay shiny and undamaged even when he walked into a barrage of blaster fire.
After Sabine observed that the Darksaber is deceptively heavy, Kanan explained that energy follows through the blade, with the wielder directing its current of power. The wielder's thoughts and actions flow into the Darksaber to fuel this energy, affecting the weight.
The Darksaber was also capable of parrying a blow from a lightsaber, with the blades being drawn to each other in an almost magnetic pull. Like other typical lightsabers, the Darksaber could not cut through pure beskar, however, it was capable of heating it to the point of turning red.
The purest form of beskar was capable of repelling the strikes of a lightsaber for brief amounts of time, and could withstand direct blaster fire. Pure beskar could still be damaged by weapons also made out of beskar; because of this, making weapons out of beskar was considered illegal by the Children of the Watch.
Obsidian in the armor supercharged Vader's dark side power, turning anger into a power source. The Empire couldn't use beskar in the armor due to a lack of knowledge on forging the Mandalorian alloy.
From something as small as a pauldron, which Din once removed to ease Grogu to sleep in The Mandalorian season 1, to an entire suit of armor as Sabine is seen doing in Ahsoka, a Mandalorian is allowed to remove their armor.
Affiliation. Boba Fett's armor was a suit of customized Mandalorian armor worn by Boba Fett, a human clone who became a bounty hunter. The armor was made from beskar.
Why can Bo-Katan use the Darksaber better than Mando?
Naturally, the same rules of the Darksaber apply to Bo-Katan, though she wields the weapon with ease against Djarin's captor. This is presumably because Bo-Katan possesses much greater confidence about her identity, even when she has lost faith in her mission to restore Mandalore.
It's possible that Gideon used the pure beskar from a fallen Mandalorian in order to craft his own helmet from scratch, or he just used it as is. It's also a possibility that Esposito's villain is using the same general helmet of a dead Mandalorian but made some alterations to it along the way.
The Mandalorians agree, and Bo-Katan is seen as the leader of her people for the first time since the Great Purge. Bo's wielding of the Darksaber was instrumental in retaking Mandalore, despite the legendary weapon being destroyed by Moff Gideon during the fight.
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.
When he passes away, it gets passed down through inheritance to his son, Luke Skywalker. So technically. the Darksaber belongs to Luke Skywalker rightfully.
Jango Fett's armor was partly made of durasteel, and General Grievous had some parts of his body made of this material. Darth Vader's armor was mostly made of durasteel, as was Boba Fett's before he upgraded during the Second Galactic Civil War to armor made of beskar.
(Fun fact: According to Star Wars canon, Phasma's armor isn't beskar either. It was actually made using scrap metal taken from Emperor Palpatine's old yacht.)
While there is no in-universe canon explanation to justify that change in the Jedi's clothing, the Star Wars Expanded Universe established that wearing bulky armor could slowly interrupt the Jedi's connection with the Force.
At the time of The Mandalorian story, it is pretty clear that Moff Gideon is not a Sith Lord even though he has the Darksaber in his possession nor does he have any links to the Jedi. Moff Gideon is nothing more than one of the Empire's existing bad guys who officially worked for the Imperial Security Bureau.
Ironically, the more Din Djarin uses the Darksaber the greater those issues likely become, because he knows this weapon should be used by the ruler of the Mandalorians - and he doesn't feel up to that task.
