How is the lyrics of the song "A woman of the world" related to Daisy Buchanan

"When she was just a girl she was a woman of the world". In this line, this presents the transition of moving up into the upper classes. This was helped by marrying Tom Buchanan. Hence Tom is an old rich, therefore his popularity is very high.

"Small talked her way round just the sort". This presents that Daisy uses her power and money to get her out of trouble such as when she kills Myrtle, she blames Gatsby for killing and everyone trust her due to her power and status with Tom.

"Of playboy's playground she'd once dream about"
The lyrics link to how Daisy chose to ignore Gatsby and married Tom Buchanan instead. Tom Buchanan is, in a way, a playboy who prefers to mess around in life and making love someone else other than his wife. Daisy married Tom not for love but for his materialistic possessions.

"Maybe I loved her but I'm jealous of her". In this case, "I" is Gatsby and "her" is Daisy. Gatsby is jealous of not having her because she wants old money, not money made from bootlegging

"She's a fake. Sure but she's a real fake"
I think this implies Daisy has conspicuous consumption to show her class and wealth, but in reality, she is really that wealth and that high in status.

"Maybe I'll be suffer, just to be her lover"
"Just to be part of her world"
Gatsby has worked hard as a bootlegger, to achieve the wealth would eventually catch Daisy 's attention and win her over. Gatsby went through so much trouble to win Daisy back that he had to join illegal dealing of alcohol.

"Maybe I'll kill her, just trying to thrill her if she don't kill me first"

Daisy is overwhelmed by Gatsby's riches and she thinks it's impossible to have all the money. In the end , Daisy killed Myrtle, blaming Gatsby's leading to George, Myrtle's husband, killing Gatsby