Best practices for spacing in the cases/matrix environment and use of \dfrac into \[...\]

I have this MWE:

\documentclass[a4paper,12pt]{article}\usepackage{mathtools,amssymb}\begin{document}\[ \begin{cases} \frac{\partial f}{\partial x} =& 2x(1 - y)=0 \iff x = 0 \quad \text{o} \quad y = 1 \\\frac{\partial f}{\partial y} =& (x^2 + y^2)(-1) + 2y(x^2 + y^2)(1 - y)=0\end{cases} \]\[H(x,y)= \begin{bmatrix} \frac{\partial^2 f}{\partial x^2} & \frac{\partial^2 f}{\partial x \partial y} \\ \frac{\partial^2 f}{\partial x \partial y} & \frac{\partial^2 f}{\partial y^2} \end{bmatrix} \]\[ \begin{cases} \dfrac{\partial f}{\partial x} =& 2x(1 - y)=0 \iff x = 0 \quad \text{o} \quad y = 1 \\[10pt]\dfrac{\partial f}{\partial y} =& (x^2 + y^2)(-1) + 2y(x^2 + y^2)(1 - y)=0\end{cases} \]\[H(x,y)= \begin{bmatrix} \dfrac{\partial^2 f}{\partial x^2} & \dfrac{\partial^2 f}{\partial x \partial y} \\[10pt] \dfrac{\partial^2 f}{\partial x \partial y} & \dfrac{\partial^2 f}{\partial y^2} \end{bmatrix} \]\end{document}

Why to have the equations separated both in the cases environment and for the hessian matrix I have to insert a space [10pt]? Why within \[ ....\] must I force to have a normal fraction use the command \dfrac?