(I hate using someone else's image but this is honestly the best way to describe them)

Seems there have been a few requests for me to do a report on the Sword-Singers. Having only just recently learned about them myself - within the past year or so - I'm not sure exactly how much I'll be able to find, but I'll do my best to answer your questions.

As always, we're going to begin with "Who are the Sword-Singers?"

(Redguard sword/shield concept art)

The Sword-Singers were an order of warriors from ancient Yokuda - the ancestral home to both Redguards and a now extinct people of mer called the Lefthanded Elves; it was east of Tamriel and it sank into the sea early in the First Era - who followed The Way of the Sword. They spent years on strengthening their bodies and their minds and were thought to be so skilled with the blade, their swords literally sang in battle, hence the root of their name. Though sword singing originated in Yokuda, it was brought over to Tamriel in the early First Era by the Ra Gada - the Wave of Warriors - when the Yokudans migrated into Hammerfell. The Sword-Singers were instrumental in the expedition of Hammerfell and helped to establish it as a new home for their people.

(a map of Yokuda in reference to Tamriel)

In ancient times, the Yokudan were not warriors. They were artisans. They were poets, artists, craftsmen, dancers, mystics, and scholars. However, early in their history, civil wars plagued their land, leading many to seek enlightenment through The Way of the Sword which was also called Song of the Blade and it eventually evolved into Sword-Singing. The Sword-Singers were confident in their belief that the sword was superior to all other types of weapons. In fact, they poured so much of themselves into their swords - their creativity and craftsmanship and their artisan techniques and their magic - that the people they were before the wars survived in their swords.

(one depiction of a Shehai)

The Sword-Singers built temples to the gods of war and training halls named the Hall of the Virtues of War in which they could practice their combat skills and the art of forging powerful swords. They worshipped and revered warrior-gods such as Onsi, who showed early Yokudans how to pull their knives into swords; Diagna an avatar of the Hoon-Ding who brought them weapons made of Orichalchum; and Leki, the goddess of aberrant swordsmanship who introduced the singers to the Ephemeral Feint maneuver. The Sword-Singers initially recruited from among the offspring of noble families. New members were accepted into the order at age eleven. Males became known as Brothers of the Blade while females earned the title Maidens of the Spirit Sword. In later centuries, mastery of the Way was achieved upon completing the Walkabout—a wilderness trek emulating the life of Frandar Hunding, where singers would wander the countryside defeating monsters and aiding the citizenry in the name of virtue. The Walkabout could take years to complete and some singers didn't survive the trials.

(Leki's Blade, a training school for Sword-Singers and Ansei)

Though the Sword-Singers were never a numerous people due to their harsh way of life in the deserts of Yokuda, they had a significant influence on their kinsmen, the other Yokudan. Their degree of devotion to each other and their philosophies saw that, after only a few generations, the Way of the Sword was ingrained into the lives and cultures of the Yokudan. The singers maintained that their swords were merely an extension of their bodies and souls, that it was the swordsman, not the sword, that mattered. 

(an ancient Ansei temple still protected by the spirits of the Ansei)

The greatest among the Sword-Singers were called Saints of the Sword, or Ansei in Yoku. The Ansei were capable of forging swords from their souls, without needing metals. This manifestation of their spirits was called the Shehai, or Spirit-Sword. They could physically impart their spirit energy and form an etherial blade in their hands. This philosophy came to be called Shehai Shen She Ru or The Way of the Spirit Sword. Every Sword-Singer devoted their life to mastery of the Way, striving to create a Shehai and become Ansei but most were never able to accomplish this task. Those who did became Ansei and were said to transcend mere mortals, having such devotion to the gods that they were seen as divine.

Ansei who gave up traditional war materials and their prized possessions became First-Rank. Their Shehai were decscribed as misty, pale, and even incorporeal. They had to give up all material possessions and devote themselves fully to their Shehai. Those who succeeded no longer needed conventional weapons, becoming Second-Rank Ansei. To become an Ansei of the Second-Rank or higher, one must not only be able to create a Shehai but also use it in combat. These were called Second-Ranks, and their Shehais burned far brighter and more brilliantly than the Shehai of those who could only create them, not use them. Their ethereal blades could cut through anything and they were called an unstoppable force of will. The only way to disarm an Ansei was to sever his hand or his head. The most elite Ansei wandered the lands, righting wrongs, solving disputes, saving their people. It was said the Shehai came to them as naturally as breathing. When the constellation of the Warrior temporarily took a mortal form in the Second Era, it was said he wielded an extremely powerful Shehai that was capable of projecting shockwaves and magickal storms.

(the Celestial Warrior and his Shehai)

In the days of ancient Yokuda, there was always a divide between the Sword-Singers and everyone else. Though much of tension was diffused at one point, Randic Torn, the Yokudan Ruler at the time, revived the strife by introducing Torn's Hunt of the Sword. This new principle ruled that only the Sword-Singers could carry swords, which further drew them apart from everyone else. When Randic Torn died, a vicious civil war broke out. During this civil war, Frandar Hunding, regarded as the most accomplished Sword-Singer in all of history, was matured.

(Frandar Hunding)

Hunding was so skilled in swordsmanship that by the age of fourteen he could use his abilities to provide for his mother and four brothers. When the war broke out, Hunding was still a young man, but a formidable sword-singer in his own right. By the age of thirty, he had gained such skill and mastery that he finally stopped using the real swords and began using the Shehai. In order to pass on his insights and knowledge, he wrote his own philosophy on The Way of the Sword. Named the Book of Circles, it was seen as the definitive manual for sword-singers in the centuries that followed.

(Book of Circles Forging Maxims)

In 1E 780, Emperor Hira attempted to take control of Yokuda by exterminating the Sword-Singers. Hunding, the Hero of the Sword-Singers, led a rebellion against Hira, despite the fact that the singers were so few in number and so scattered they could not form much of an army to resist. Hunding's rebellion became known as The War of the Singers. Hunding was victorious but less than twenty-thousand singers survived. Hunding was outcast by his people and he and his army left Yokuda, migrating into Hammerfell.

(a member of the Hiradirge)

A few years after Hunding left, Yokuda sank into the sea. Some say the land mourned its greatest hero, but the Yokudan believe it was a specific group of powerful Sword-Singers called the Hiradirge, who were said to wield stone magic and could move the land itself. In the last civil war, they were defeated and it was said they took their revenge by destroying Yokuda itself. In fact, the mortal form of the Celestial Warrior corroborated this legend by saying it was a Shehai of a powerful Ansei who destroyed Yokuda, calling the stroke the Pankratosword - a sword stroke so powerful from an equally powerful Shehai that it could cut through the laws of nature themselves.

(a member of the Hiradirge)

After Yokuda's destruction several waves of refugees and warriors, known as the Ra Gada, fled to Hammerfell. Among them were accomplished sword-singers and Ansei, such as the famous Yaghoub's Thirteen, King Xakhwan's army of sword-singers, or the fabled group of master Ansei known only as The Four. Formidable singers such as these claimed the entire province and established a new home for the Yokudans.

(warriors of the Ra Gada in ESO)

Schools and training grounds were established and a group of warriors called the Anka-Ra ventured into Craglorn and established the Hel Ra Citadel which was thought to be a temple devoted to the training of Ansei. Others established the Abbey of the Blades and the Rahni'Za, School of Warriors. Rahni'Za, supposedly dedicated to the Warrior constellation, trained students to become Sword-Disciples by completing five increasingly arduous tests of strength and skill.

(Dragonguard Sai Sahan at an Ansei crypt within the Hel-Ra)

When Hammerfell faced a great threat from a group of powerful elven necromancers, the Ansei heroes Majah, Radan, and Halelah sacrificed themselves to protect the people from the risen dead. As part of a covenant with Tu'Whacca, each Ansei channeled their spirit into the blade they wielded in life. These swords became known as the Ansei Wards, and would protect the land from even the most powerful necromancy.

(an Ansei Ward)

After conquering Hammerfell, the Yokudan fell into an era of peace. During this time, many warriors laid down their swords, vowing a life of complaceny and pacifism to rebuild their broken people and nation. Within only three generations, the Book of Circles was abandoned and the teachings of The Way of the Sword faded into legend. Ansei became all but myth, the various schools still stnading but rarely ever producing a warrior who had mastered the Shehai. However, many renowned warriors did still exist, such as Gaiden Shinji and the Ansei Makela Leki.

(Derik Hallin, the Last of the Ansei)

When Hammerfell came under attack from giant goblins through a rent in space, the Queen of Ojwambu pleaded with Derik Hallin, the Last of the Ansei, begging for his aid. It is said he called upon the spirits of long dead Ansei to aid him in his battle. Dozens of Ansei warriors appeared beside him and fought until they were victorious. Others say he instead scoured the land for five Ansei relics and used them to defeat the goblins, during the time of Divad Hunding. Whatever really happened, Halling saved Hammerfell and restored the teachings of Frandar Hunding to his people.

(Divad Hunding in ESO)

Unfortunately, this was not to last. As time passed, despite the continued honor of The Way of the Sword, the number of Sword-Singers slowly dwindled until barely more than a handful were left. By the mid-Second Era, there were no records of any Ansei left and Redguards came to believe that the Shehai was a myth, scholars even dismissing it as superstitious nonsense. By the Third Era, even the Ansei were thought to have never existed. It is unclear how this happened, as the training schools were not only still honored and kept, but were still used. The Ansei simply died out. By the Fourth Era, no trace of the Ansei remained except in the Redguards themselves, as they were still the most capable warriors in all of Tamriel.

(concept Redguard warriors)

I spent the last two weeks stockpiling information from across the UESP and Reddit to get this information. I hope I answered your questions and satisfied your curiosities.