Believed to be the most deadly fighters on the continent.

That's simply incorrect. Myrddraal outrank them, especially when carrying Fadeblades. Also, consider the following from Rhuarc's account of five Aiel against three Fades (one injured): "They would have killed two or three of us, certainly, perhaps all, and I cannot say we would have finished them all."

Aiel background during the Breaking
There may also have been a Fortelling that the Aiel would eventually produce a man who would stand against the Dark One. ....therefore the AS devised a great task worthy of the Da'shain, because they knew that no lesser task would convince them to leave.
The Second Covenant, occasionally spoken of by Aiel and Tinkers probably refers to this last duty the Aes Sedai laid upon the Aiel.

I didn't know that the Tuatha'an knew anything about the Second Covenant, I'm surprised that someone hasn't tied them together with the Aiel.
Also I wonder how the Tinkers feel about breaking the Second Covenant ?

Development of the Spear Fighters
There are indications that the first of the Maidens, Morin, had a Fortelling, that she would bear a child to the warrior chief Jeordam, which she did, thus beginning the process that allowed the tent-dwelling Aiel to sustain a self-reproducing culture on their own.

I wonder how long it took for there to be no One Power capable Maidens ?

It was sometime just after the crossing into the waste that they began dividing into clans and septs.
No set number of septs comprise a clan.

Development of the Jenn Aiel
The Jenn Aiel eventually adopted the derisive name given to them by the tent-dwellers.
Rhuidean - design probably inspired of Aes Sedai memories of cities before the Breaking.
The lake of Rhuidean in turn feeds the only known river in the Waste, which brings water to lands which have known only drought since the time of the Breaking.

Prophecy
The Aes Sedai realised that they had made a mistake, if a child was born of the Aiel to fight the Dark One, he would not be born of the Jenn, But the Aes Sedai had no ties with the nomadic Aiel warriors.
In order to save the prophecy, and perhaps Aes Sedai control of it, they had to find a way to share the truth with the warriors in a way that would not destroy them.
Those who returned, only one in three, had demonstrated the strength to face the truth of their heritage.

Clothing
The only difference between the grab of male warriors and that of other Aiel men is that the warriors carry a longer knife.
Women who are not maidens, wear their hair shoulder length and longer, but rarely braid it or gather it up.
High ranking women are likely to display an abundance of jewellery.
The men wear no jewellery at all.

Further Information
Apparently nonmarital relationships are quite common.
Each sept has its own hold and within it the Roofmistress, the wife of the chief, reigns supreme.
The Aiel mine their own gold and silver, rubies, sapphires, moonstones and firedrops though do not facet cut any of these gems in their work.
There are no records of one woman marrying two men.