I don't get the scenes regarding Natalie and Leonard. How is she connected to the movie's main story and is she the one who is using Leonard to distribute drugs?
Natalie is a bartender. She is dating Jimmy.
One day she is tending bar and this guy she's never met (Leonard) shows up, wearing clothes that Natalie knew Jimmy had been wearing earlier. Leonard had come to the bar because he found its address in Jimmy's clothes.
Immediately Natalie is worried about Jimmy and suspicious of Leonard. Eventually she believes Leonard's story that he can't make new memories so doesn't remember anything about Jimmy.
Jimmy had owed money to Dodd, and because Jimmy is missing, Dodd starts harassing Natalie. To protect herself, Natalie uses Leonard to scare off Dodd.
Later we learn that Teddy had manipulated Leonard into killing Jimmy. Teddy did that because he wanted to steal Jimmy's money. Leonard does not remember anything about killing Jimmy.