Rolles theorem: differentiabilty open brackets significance

Question

1. https://math.stackexchange.com/a/2863979/922054 Related to Rolle's theorem : Here it is said that $f(x)$ is non-differentiable at endpoints of $\sqrt{1-x^2}$, but isn't it okay to talk of endpoint differentiability as only left handed one or right handed one only in case of end points?
   And then we can say a function differentiable in $[a,b]$ ?
2. Are there any exceptions where it might fails to work ( that is Rolle's theorem ) if we include endpoints in differentiability leaving the above example?
3. And do we say that here the $(-1,0)$ point is non-differentiable ?