Answer
No. No.
Work Step by Step
Consider an object whose moment of inertia is $I$, spinning around a fixed axis at angular speed $\omega$, with angular momentum $I\omega$. The rotational kinetic energy may be expressed as $KE_{rot}=\frac{1}{2}I\omega^2=\frac{L^2}{2I}$.
We see that for two objects with different moments of inertia $I_1$ and $I_2$, having the same angular momentum L doesn’t mean they have the same rotational kinetic energy $KE_{rot}$. Similarly, having the same rotational kinetic energy $KE_{rot}$ doesn’t mean they have the same angular momentum L.
