You've got a good handle on things from my point of view, but by looking at the system as a whole (like yoda did with the string) it leaves greater scope for misunderstanding and it is harder to identify where the misunderstanding lies.
There is a nice student exercise that beginning physics students use about a man standing on bathroom scales whilst a lift accelerates upward. I'll run through it if anybody thinks it will help, but to go back to your examples...
If you push on your car the equal and opposite reaction is that the car pushes on you with the same force and in the opposite direction. You push on the earth and the earth pushes back, but this pair of equal and opposite forces will be different in magnitude to the push on car/car pushes back. The second phase of analysis is to look at each object and ask what forces are acting. On the car, your push. On you, the car's push and the ground's push. On the ground, your push.
With the rock and the string, if the mass of the string is important then we can't perform a correct analysis without separating considering the "string on rock/rock on string" and "boy on string/string on boy" pairs separately because they will have different magnitudes. We can't just say "boy on rock/rock on boy" without things getting very muddled.
This is where the man on scales in lift will help if you need more detail.
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