Why is the law of conservation of linear momentum considered fundamental and universal?

$A$ stationary body explodes into two parts of masses $M_{1}$ and $M_{2}$. They move in opposite directions with velocities $v_{1}$ and $v_{2}$. The ratio of their kinetic energies is

$A$ person of mass $80 \ kg$ is standing on a trolley of mass $320 \ kg$. The trolley is at rest on a frictionless horizontal rail. If the person walks on the trolley at a speed of $1 \ m/s$,what will be their displacement relative to the ground after $4 \ s$?

$A$ ball is projected at $60^{\circ}$ from the horizontal at $200 \, m/s$. At the maximum height during its flight,it explodes into $3$ equal fragments. Out of these,one part travels at $100 \, m/s$ vertically up while another travels at $100 \, m/s$ vertically down. What will be the speed of the third part just after the explosion?

$A$ ball of mass $m$ is moving towards a wall with velocity $v$ at an angle $\theta$ with the normal to the wall, as shown in the diagram. In which direction is its linear momentum conserved?

$12 \,kg$ bomb at rest explodes into two pieces of $4 \,kg$ and $8 \,kg$. If the momentum of the $4 \,kg$ piece is $20 \,Ns$, what is the kinetic energy of the $8 \,kg$ piece (in $\,J$)?