Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the matrix:
$$\begin{bmatrix}1 & 2 & 0 & 0 & -7 & 3\\0 & 0 & 1 & 0 & -3 & 3\\ 0&0&0&1&3&26\\0&0&0&0&0&1\end{bmatrix}$$
My answer would be: $$X= x_2\begin{bmatrix}-2\\1\\0\\0\\0\\0\end{bmatrix}+ x_5\begin{bmatrix}7\\0\\3\\-3\\1\\0\end{bmatrix}$$
Is that correct? if not, can you explain why?
Yup, they are correct.
The nullity is $2$ since there are $4$ pivot columns and those two vectors are indeed form a basis.