Here I might as well explain the relationship between the Grim Reapers and Shiko's family.
They are two separate families. The Grim Reapers represent death in general, and justice for those who have strayed to the side of evil. The Devils, for a lack of a more creative name, are their RIVALS who represent unjustified death.
The Grim Reapers tend to take only evil souls. The Devils take pure and innocent souls, so they're often seen as evil.
Shiko's father (literally Satan) is the king of hell. Shiko is the princess, but since she has older brothers she is not the heir. She's a bit of an outcast in the family, preferring to only collect evil souls like the Reapers do. So she goes to DWMA seeking refuge.
Death is hesitant to accept her, but her soul appears to be more pure than the rest of her family so he allows it. Shiko is enrolled as a weapon, but does not have a meister.
Since she is the child of a really powerful family, she is strong enough to split her soul and become both weapon and meister at the same time. In this form, she appears normally but additionally summons her weapon form, which she can then use as a normal weapon.
Death the Kid is at first really ticked off at the fact that she was allowed in, both because of her family's reputation and because she has no meister. She then takes a particular liking to teasing him and he might develop a slight crush. Their soul wavelengths are compatible, so Kid could use her if he had to, although he would hate the imbalanced weapon and Shiko wouldn't appreciate being used by a meister.