Determine unhampered natural frequency and motor constants from graph?
Commonly used ROT for a standard 2nd order TF (no finite zeroes) are:

Time to 1st peak: \$t_p =\large\frac{\pi}{\omega _n\sqrt{1-\zeta^2}}\$

\$\small \pm 2\%\$ settling time: \$\small T_{S2} \approx \large\frac{4}{\zeta \omega _n}\$

\$\small 10\%-90\%\$ rise time: \$t_r \approx\large \frac {1\:+\:1.1\zeta\:+1.4\zeta^2 }{\omega_n}\$

Peak overshoot to a unit step input: \$\small M_{pt}=1\:+\:\large e^{\small{-\zeta \pi}\large/\small{\sqrt{1-\zeta^2}}}\$

For parts (b) and (c), you might work out the CLTF of the block diagram and compare coefficients with the standard 2nd order TF and ROT