The demiplane spell creates a demiplane that appears to be an empty room 30 feet in each dimension, made of wood or stone.
Are these walls actually made from wood and stone? Can a character chip off a piece of stone? A sliver of wood? Would it be possible to hide in them using the meld into stone spell if they are of stone?
Demiplane doesn't have walls in conventional sense. It just ends, looking like a wall to an observer (or like something else, according to the nature of specific demiplane).
According to Player's Handbook:
Demiplanes are small extradimensional spaces with their own unique rules.
A given demiplane can be entered through a single point where it touches another plane.
So, other than the door, it's not touching any other dimension. There is absolutely nothing through the "wall" of demiplane. No other plane, no space, no vacuum, nothing.
So the "material" of a demiplane, created specifically by Demiplane spell, is just an aspect of it, shaped by the spell (presumably for caster's convenience and sanity). It has no actual matter or thickness to it and doesn't separate demiplane from anything, since there is nothing on the other side. There is no other side altogether.
As stated in the description:
When opened, the door leads to a demiplane that appears to be an empty room 30 feet in each dimension, made of wood or stone.
The whole thing is a facade. It just looks like a room constructed of wood or stone. So you can't use any spells on/against the walls that require actual wood or actual stone.
The Demiplane spell’s description states:
(…)demiplane that appears to be an empty room 30 feet in each dimension, made of wood or stone.(…)
Appears to be meaning that it’s not really a room with wood or stone walls, it just looks like one. Since the spell only mentions appearance, I think it’s reasonable to assume that the walls only look like they’re made of stone, they don’t actually behave like stone walls (since you know, the spells-only-do-what-they-say-they-do thing). You probably then cannot either hide in them or chip anything off.
As to what exactly they’re made of and how they behave, I’m afraid there isn’t a lot of information. The walls are the boundaries of the demiplane that the spell creates but there’s not a whole lot of info on demiplanes in 5E, the only mention I found was in DMG, p.68 and all it says that might be relevant is that demiplanes are extradimensional spaces and can be as small as a single chamber. The whole demiplane is made of magic, so the boundaries probably are too but that’s as much as you can definitely state.
