$Fe$ (atomic number $= 26$) atom has the electronic arrangement:

The explanation for the presence of three unpaired electrons in the nitrogen atom can be given by

When the azimuthal quantum number has a value of $l = 0$,the shape of the orbital is

Which of the following are correct?
$(1)$ Electron density in $XY$ plane for $d_{x^2-y^2}$ orbital is zero.
$(2)$ The energy of $3p$-orbital is higher than the energy of $2p$-orbital.
$(3)$ $3p_z$-orbital has one angular node.
$(4)$ $4f$-orbital has no radial node.

Number of nodal centres (radial nodes) for $2s$ orbital is:

According to which principle is the electronic configuration of nitrogen $1s^2 2s^2 2p_x^1 2p_y^1 2p_z^1$ and not $1s^2 2s^2 2p_x^2 2p_y^1 2p_z^0$?