In the manga all the things that weren’t shown in the anime were explained in good detail. One example (Spoiler ahead~): Haibara’s puppet was used to cheer up Kozue when she was a little girl, he originally took care of her after her parents died.
Also, Nanako (despite her name) is actually 6 years old. Oh, and the ending song that you didn’t like- Boku no Speed de, was about overcoming struggles and life. It was able to relate to the anime because it showed a change for Kozue, her friends being able to help her (as well as her split personalities) after her parents died- Haibara, Sayoko and Asami, Tamami, Momono, and of course Shiratori in the end. That was really what the song was about. The opening song dealt more with the day-to-day meaning of the storyline. While it was a slice-of-life, the plot emphasized (and could be seen more in the manga than anime) the romance between Shiratori and Kozue.