Mostly applies to new characters, though I can see the stone being useful regardless. Maybe suvival, maybe carpentry for wood, I have no idea which would be better suited for it so I won't pretend. As for stones, survival just seems the best fit.
Let them have a minor effect on quality. Explained by someone good at survival/carpentry having a better knowledge of the wood/stone, and so being able to chip/chop better shaped stones and less deformed branches. Having a branch without a ton of knots in it would be much easier to work with and provide a better quality finished good. Same deal for stones - Someone more knowledgeable with them would be able to find areas with a better shape, and be able to chip it without weakening the stone via cracks.
Mainly a way for there to be some variation in natural trees and stones, and it gives new characters access to slightly higher quality equipment. Planting your own is still vastly preferable, but if you spend a little extra time gathering branches and picking out the best quality, you get a slightly better table to start off with etc.
Shouldn't affect it much, and higher skill levels should affect it less. Ten survival might give an extra 1-5 quality (Its wants to be random for the variation aspect, see?), but going from 100 to 110 might not give any, or only a possible 1 extra. Once again, I'm too new to come up with good numbers for the quality, but you get the idea. Every stone in the world shouldn't be the same, and everybody shouldn't be exactly as good at chipping away parts of it.