Which of the following statements are true?

If $D(2, 1, 0)$, $E(2, 0, 0)$, and $F(0, 1, 0)$ are the mid-points of the sides $BC$, $CA$, and $AB$ of $\triangle ABC$, respectively, then the centroid of $\triangle ABC$ is:

The midpoints of the sides of a triangle are $(1, 5, -1)$,$(0, 4, -2)$,and $(2, 3, 4)$. Find the centroid of the triangle.

In a triangle $ABC$, if the midpoints of sides $AB, BC, CA$ are $(3,0,0), (0,4,0), (0,0,5)$ respectively, then $AB^2+BC^2+CA^2=$

Let $A(x, y, z)$ be a point in the $xy$-plane,which is equidistant from three points $P(0, 3, 2)$,$Q(2, 0, 3)$,and $R(0, 0, 1)$. Let $B = (1, 4, -1)$ and $C = (2, 0, -2)$. Then among the statements $(S1) :$ $\triangle ABC$ is an isosceles right-angled triangle and $(S2) :$ the area of $\triangle ABC$ is $\frac{9 \sqrt{2}}{2}$.

If the origin is the centroid of a triangle $ABC$ having vertices $A(a, 1, 3)$,$B(-2, b, -5)$,and $C(4, 7, c)$,find the values of $a, b, c$.