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.

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.

noun. 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.