In the first part:

Momentum will be conserved so \(\displaystyle P_f = P_i\). We know that there is a kinetic energy loss, so \(\displaystyle KE_f = f \cdot KE_i\).

Choose a positive direction to the right. I'm going to say that car 1 is moving to the right initially. I'm going to call the initial velocities of the cars \(\displaystyle v_1\) and \(\displaystyle v_2\). Here's the setup:

Momentum:

\(\displaystyle m_1 v_{1f} + m_2 v_{2f} = m_1 v_1 - m_2 v_{2f}\)

and Energy:

\(\displaystyle \dfrac{1}{2} m_1 v_{1f}^2 + \dfrac{1}{2} m_2 v_{2f}^2 = f \cdot \left ( \dfrac{1}{2} m_1 v_1^2 + \dfrac{1}{2} m_2 v_2^2 \right )\)

You know that \(\displaystyle m_1 = m_2 = m\) and \(\displaystyle v_2 = v_1 = v\).

See what you can do with this and let us know what you've been able to do.

-Dan