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

The momentum of a system is conserved:

$A$ spaceship of speed $v_0$ travelling along $+y$ axis suddenly shoots out one-fourth of its part with speed $2v_0$ along $+x$ axis. The $xy$ axes are fixed with respect to the ground. The velocity of the remaining part is:

An artillery piece of mass $M_1$ fires a shell of mass $M_2$ horizontally. Instantaneously after the firing,the ratio of kinetic energy of the artillery and that of the shell is:

$A$ spring is compressed between two toy carts of mass $m_1$ and $m_2$. When the toy carts are released,the spring exerts equal and opposite average forces for the same time on each toy cart. If $v_1$ and $v_2$ are the velocities of the toy carts and there is no friction between the toy carts and the ground,then :

$A$ man of mass $m$ is standing on a platform of mass $M$ kept on a smooth ice surface. If the man starts moving on the platform with a speed $v$ relative to the platform,with what velocity does the platform recoil relative to the ice?