In the old days ladies used to SWOON - it meant to faint, collapse, become unconscious.
They needed to be revived with smelling salts, cups of tea, and sympathy.
Why did they swoon? Usually because they's just met a terribly handsome man and they were overcome with ....... whatever!
So I guess you can work out what a swooning song might be like: romantic, slow and melodic maybe.
As the 'the likes of' - it means 'similar to' 'of the kind/sort/type'
It can be used in the singular - Albert Einstein! What a genius! You'll never see the like of him again! It works in the plural too: You'll never see the likes of him again.