Why are anime girls drawn without pubic hair? Why are there no hair drawn down there or anywhere apart from FEMALE character's heads in anime? 
I heard it was illegal from my friend. Were they making it up?
I believe Japan's obscenity laws have some particular rules regarding pubic hair. Also, often hentai artists prefer a hairless body for their particular demographic / fetish / etc.

Up until the mid 1990s, pubic hair had to be censored in Japanese media. The law has been relaxed since, but as it had been common to do without hair, many artists continued with it.

Saying that, there are some hentai works that contain pubic hair - but whether they are complying with the law is another topic, as mangaka's regularly 'interpret' the law loosely. Such as opting for a very minimal censor bar:



A female version would be similarly censored to a minimal interpretation of the law. Unfortunately I don't have any appropriate pictures of fruit on hand.

Further Reading

An Overview of Censorship in Anime (This is my own article on the subject, broadly covering the topic)

"Obscenity, Pornography, and the Law in Japan:
Reconsidering Oshima’s In the Realm of the Senses" (Heavier in content, but perhaps more specific for your question)