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.

The ATC takes a secondary set of skills to lower someone [while belaying] from a long distance from above.” Both devices are capable of accommodating high-risk situations, but the GriGri is more likely to switch between uses at a faster rate, which can be essential in extreme or life-or-death situations.

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.

A Grigri (styled as GriGri or GRIGRI) is an assisted braking belay device manufactured by Petzl designed to help secure rock-climbing, rappelling, and rope-acrobatic activities. Its main characteristic is a clutch that assists in braking under a shock load.