Check out this excellent post from Amaterasu's Son
Madara once said will cannot be passed down.
I propose that he was right to a degree. Obito never met the Rikudo
Sennin, he never saw him with his own eyes, he never heard his voice
or touched his heart. Rikudo Sennin couldn't pass down his will to
him.
"His passion and intensity, permeate throughout the blade...you could
say this blade carries his very essence."
Therein lies the problem.
Obito has no passion. He has no intensity. He has purpose, he has
desire, and he has determination. But emotionally? He's an empty husk
scratching to reclaim his own life as he envisions it.
But Obito cannot use that sword. You can't borrow Rikudo Sennin's will
and passion and subvert it for your own use. If what Obito said was
absolutely true then that sword breaking was absolutely foreseeable.
Lest Obito forgets Hagoromo chose his younger son to lead the way to
the future. Of the little we know about Rikudo Sennin we know that he
has already rejected Obito and Madara's past thousands of years before
they were even born. So if it is his essence in that blade, then
clearly it broke on purpose because it wants Obito to lose.
If Obito was simply speaking metaphorically then it broke because he
does not have the will and emotional vivacity to use such a weapon.
For a man with no heart and no identity, using a sword that was
supposedly comprised of passion is completely impossible.
Peace.
In other words, the Sage used his sword to create the world, life, friendship, etc. Obito is trying to use the sword to destroy all of that, but the sword simply cannot be used for those purposes. This is why the sword broke.
UPDATE: I realized this answer isn't entirely answering your question and that is partially because there are no definitive answers to your first 2 questions. Unfortunately, I don't know about Japanese/Chinese history to answer the third.
To answer the first, I believe anyone who has similar powers to the Sage of Six Paths can create one. So far, we have seen Obito wielding Rikudou Sennin's, Madara with his own, and this might be a stretch, but Naruto+Sasuke with their mighty sword.
Basically, the sword is a materialized version of the creator's will. By this, I mean that one of the requirements to make this type of sword is a very powerful will from its owner. I believe the sword Naruto had defeated Obito's sword was only because Naruto's will was stronger than Obito. Similar to what Amaterasu's Son was saying, I think Obito and his sword was not as powerful because the user himself did not have the will of fire.
Now let's talk about the abilities of this sword. All we know is that Obito said the Sage of Six Paths created the world with this sword. Madara's version for Obito also had his will in the sword. So despite not knowing exactly what the abilities are, we know that the sword's abilities will help accomplish their goals / will. Rikudou Sennin's sword was to create the world of peace, so that is what his sword abilities will complement. Although we don't know what exactly Madara's goal is yet, we do know he has some sort of evil plot to control the world. His sword will help him accomplish that goal, which is why he also passed it on to Obito.
Analysis / discussion link to Madara's materialized will here
