2. The above point is actually moot since the application of Conservation of Momentum is NOT valid since there are external forces (how else are the skid marks produced?) acting on the system.
More information (such as the length of the skid marks) is necessary before the question can be correctly answered.
3. If you mean by perfectly plastic that the cars are stuck together after the collision, then of course it follows that . But you're told the cars are stuck together after the collision ...... why confuse the issue by talking about perfectly plastic collisions .....?
And you do realise that the collision is not elastic, right?