There’s a little flimsy poppet that gets pushed up and seals on the circle when there’s water pressure. A couple years ago I fixed one at my parent’s house where the poppet was simply out of position.

Frostproof hose bibs go deep into the wall. Replacing will likely involve cutting into the wall.

They definitely were. Margaret Killjoy did a couple episodes on her podcast about them with John Darnielle from the Mountain Goats if anyone would rather listen than read about them.

The knob should just pull off, but sometimes they require full chooch. If she breaks it, it’s not a big deal. If Habitat Re-Store is a thing near her they usually have a shelf of these knobs for almost nothing. If not the big box stores sell them too, and the lights can be turned on and off without the knob until she can get a replacement.

Back when I worked as a handyman I used the old knobs for many things. Some people get very weird about change. I’d usually ask if they wanted the new one to wedge into their junk drawer, though.

Hollow doors have about a 1" frame of solid wood around the perimeter.