The Gri-Gri will act as something of a “second-hand,” even if the worst should happen and the brake strand is released. Regardless of the context – sport, trad, multi-pitch, single pitch, trad, alpine – it is inherently safer than the ATC.

gri·​gri. less common spelling of gris-gris. : a talisman, amulet, voodoo charm, spell, or incantation believed capable of warding off evil and bringing good luck to oneself or of bringing misfortune to another.

Rappelling with the GRIGRI can be done on EN 892 dynamic or EN 1891 low stretch rope of a compatible diameter indicated on the device. There are several ways to set up the rope for rappelling: they are described in the technical tip, Multi-pitch rappelling with a single rope.

Daughter is using a Grigri as a self-belay device. This is expressly discouraged by Petzl, the manufacturer, on this page titled Self Belaying is Prohibited. That's pretty damning. As the page admits, some people do use a Grigri for self-belays, but it's not ideal and potentially dangerous.