Charge conservation is the principle that electric charge can neither be created nor destroyed.
Yes, though it might be good to mention net charge. We can create charged particles in pair production and destroy them in annihilation.
In electromagnetic field theory, vector calculus can be used to express the law in terms of charge density ρ (in coulombs per cubic meter) and electric current density J.
Ah, but if ever you point to a law, somebody somewhere will be sure to break it.
Charge conservation can also be understood as a consequence of symmetry
And physics is full of broken symmetries.
through Noether's theorem, a central result in theoretical physics that asserts that each conservation law is associated with a symmetry of the underlying physics. The symmetry that is associated with charge conservation is the global gauge invariance of the electromagnetic field. This is related to the fact that the electric and magnetic fields are not changed by different choices of the value representing the zero point of electrostatic potential.
But don't forget that the field is the electromagnetic field. An electric field is what you call it when you only see the linear force between charged particles, a magnetic field is what you call it when you only see the rotational force between charged particles.
Is there some experiment that shown if can possible some charge electron, or spin violation?
Not that I know of. But charge is related to spin and angular momentum. We usually think of angular momentum as being conserved. But if your spinning disc is smashed to pieces, parts fly away linearly in all directions. The angular momentum appears to have vanished. I expect that there will one day be some electromagnetic equivalent wherein charge is not conserved. Gamma-ray bursters may be of interest.