what size in fractions is half of a half of half grown quarter-bone?

Answer 1

If a quarter-bone is 1/4 of a whole bone and a half-grown quarter-bone is half the size of a full-grown bone, then you end up with 1/32.
If a quarter-bone is a name for something that's still full-sized but just has an odd name and half-grown is half of a full-size, then you end up with 1/8.
And if the name means nothing and half-grown is the same size as full-grown (ear bones come to mind) then it's just 1/4.
That should cover it.

Answer 2

an eighth bone

Answer 3

(1/2)(1/2)(1/2)(1/4)=1/32