The scene of Florence's character engaging in masturbation was performed by porn actress Alisha Klass, not Molly Parker.
This film was tied to a controversy when the owner of the Esquire Theater in Cincinnati, Ohio ordered five seconds to be cut from the print of this film being shown in his theater. When this was revealed, the distributor ordered him to stop showing the censored film altogether. The critic that called him out on it was subsequently banned from the theater and it raised questions as to whether this theater (the only one in town that would show unrated or NC-17 films) had censored the films it had shown before. The theater owner defended his actions and refused to comment on such suggestions.
At about the midpoint, Florence provides an explanation for the title. She says, "We are all born out of a woman's c*nt. It is, The Center of the World."
When asked about his secret fantasy, Richard whispers something into his companion's ear. Florence snickers upon hearing it, and knowingly informs him that the Chinese calls this bit of kinkiness "fire and ice," to which he responds that he cannot believe that there actually is a name for such a wanton act. She then sets upon performing this deed. It does not get shown explicitly on screen, but it involves an ice cube, and a mouthful of Tabasco sauce.