James matured a lot in his seventh year and stopped bullying students for fun. He also became nicer to people (which made Lily fall in love with him) so Dumbledore decided to make him head boy. Remus wasn't the head boy because when he was prefect, he didn't manage to keep his friends out of trouble.

Then why is Draco Malfoy a prefect?

Prefects are appointed after consultation with the Head of the House, which in this case happens to be Snape. Most likely, Snape asked Dumbledore to make him a Prefect, to which the latter obliged, seeing as Snape was pivotal "for the greater good" (fight against Voldemort, in which Snape was a double agent/spy). @Second British Hong Kong Ball

As for James, as said above, he did change drastically in his senior year(s).

Lily never fell in love with James but oki

Um, wdym? She had married him and had a kid with him....

^Yeah- canonically, they did love each other

Sure -_-