Equals and opposites - that's the clue - just like it says.
I wasn't sure what the fireworks were about. But then I looked carefully at the rocket taking off. Then I saw the equal and opposites.
Compare the speeds of the guys when its one on one and one on two.
The "Newton's Cradle" is just a toy but it does show equal and opposites very clearly.
I suddenly realised that another way of thinking about equals and opposites is action and reaction.
Whenever you do something there is always a consequence.
The way to approach this experiment is systematically. Do experiments with the square block first of all. Alter either the mass or the velocity for just one of the blocks. Work through a number of combinations and see what happens to the velocity after the blocks collide. The final answer is not the velocity itself but it is related to a combination of velocities and masses.
And you can move the position of the blocks before starting the experiment - so they do bump into each other.

Don't forget the velocity can be set in either direction - represented by plus and minus.

This rule - this "Law" - is all about collisions - what happens when objects bump into each other.
I'd been getting confused by the effects of friction and air resistance. Once I turned them off I began to get some idea about what was happening. Then I could turn friction on again.
Concentrate on the combination of velocity and mass. Examine that combination before and after collision.
The experiment with the crashing cars does illustrate the same rule - the same "Law". But cars have engines - which are running before the crash and so they over come the friction by putting in force all the time.
Here are some comments from other pupils and teachers that may help you to investigate.

Third Law Clues