In which change do both the bond order and the number of unpaired electrons increase?

The wave functions of $1s$-orbitals of two hydrogen atoms are $\psi_A$ and $\psi_B$. $\psi_A$ and $\psi_B$ are linearly combined to form two molecular orbitals ($\sigma$ and $\sigma^*$). Which of the following statements are correct?
$I$. $\sigma^*$ is equal to $(\psi_A - \psi_B)$.
$II$. In $\sigma$-orbital,one nodal plane is present in between two nuclei.
$III$. The energy of $\sigma$-orbital is lower than the energy of $\sigma^*$-orbital.

The molecular orbital configuration of a diatomic molecule is
$\sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_x^2 \pi 2p_y^2 \pi 2p_z^2$
Its bond order is

The main axis of a diatomic molecule is $Z$. The orbitals $p_{x}$ and $p_{y}$ overlap to form:

Which of the following molecules does not exist on the basis of Molecular Orbital Theory?

The correct order of energy of $\sigma_{2p_z}$,$\pi_{2p_x}$,$\pi_{2p_y}$,$\pi_{2p_x}^*$,$\pi_{2p_y}^*$ and $\sigma_{2p_z}^*$ orbitals in $F_2$ is: