From whom did Desdemona learn the 'Willow' song? How do the song and the story Desdemona tell connect to the events of Othello?

As she turns down the bed to await her husband, Othello,
Desdemona recalls for Emilia how she heard and learned "a song of 'Willow'," from her
mother's maid, Barbary:

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My mother had a maid call'd
Barbary: 
She was in love, and he she loved proved mad 
And did
forsake her: she had a song of "Willow," 
An old thing 'twas, but it express'd
her fortune, 
And she died singing it. That song tonight 
Will not
go from my mind; I have much to do, 
But to go hang my head all at one
side, 
And sing it like poor Barbary.
(4.3.26-33)

In the same way
that "poor Barbary" found in the lyrics of the song a perfect match to her lovelorn
spirit, so too does Desdemona.  Like Barbary, Desdemona is losing her beloved husband as
a result of a kind of 'madness' bred out of an all-consuming jealousy. Presumably
Barbary died of a broken heart. Soon after the lyrics leave her lips, Desdemona will die
of that cause as well as by the hands of her avenging
husband.

Depressed, engulfed in foreboding, Desdemona's
lost love is evoked not only by the subject of the song itself, but by the image of the
'weeping willow', a tree thought to symbolize a rain of tears, or a person (likely a
maiden) hanging her hair in mourning. Thus, the words of the song speak of a "poor
soul", reclining by a "sycamore tree", weeping and moaning, her salt tears falling into
"fresh streams".

As she concludes the first verse of the
song, Desdemona, unconsciously, adds a line of her own - "Let nobody blame him; his
scorn I approve," - singing now of her own feelings, and not those of the sad woman of
the song. The embittered words of the second verse -  "If I court moe women, you'll
couch with moe men." - mirror the destiny of the hapless Desdemona. Inasmuch as
the "mad" lover of the song made his unfaithfulness his lady's fault, so too has Othello
done likewise with his wife, thus sealing her doom.