@Evan First of all, I accept Newton's laws of motion and it would be stupid to question them. Regarding my confusing sentences, I apologize. The correct sentences are:
"the system will acquire no momentum (if initially is not moving)" "the net force upon a part of the system"
Regarding all the rest you mention, please check my proposed answer (just sent) to my question. I would really appreciate any comment of yours.
Discussion on question by John: Newto…
Discussion on question by John: Newto…