1) Yes, in a system objects can have momentum while the momentum of the system is zero, for example in a system there are two particles one having equal masses but opposite velocities (the same magnitude).
2)Firstly, we have to define momentum. Momentum is define as the product of mass and velocity. Also considering the third law of motion which states that: for every action, there is equal and opposite reaction. Considering the 2nd law of motion which states that the rate of change in the momentum of a body is equal to the applied force and takes place in the direction of the applied force.
They both have same mass and velocity definitely, they will both experience same momentum. Also from the question, the both share same velocity hence, the will both hit the wall with same velocity meaning the will both feel the same impact from the wall as well. Hence the third law of motion proves this right.
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