How are Shinigamis born?
In chapter 47 of the manga, it is mentioned that 

A Shinigami is capable of reproduction, such beings possessing groins.


However, Shinigami are also capable of asexual reproduction, as explained in volume 9.


  Shinigami can asexually reproduce by creating fragments of themselves and create a being. These beings, rather then be a replicate of the parent, can spawn off their own personality