Firstly is it correct that a particles spin rate is constant? Secondly how does this relate to the charge of a particle, which is also constant?

Particles do not "spin" as you think they do. An electron is not like a little top spinning around. There are really no good analogies to describe what spin means as it relates to these particles. You must understand the math underlying quantum mechanics and quantum field theory. Specifically, you should study how Dirac explained it. As much a mathematical triumph as GR. Bohr was wrong. Classical physics does not work in the quantum realm. Electrons are not tiny spinning objects with a "spin rate".

Anyhow, the angular momentum of a particle is intrinsic. It is a fundamental quality and a base property. If a particle was truly spinning, it would be spinning faster than the speed of light to produce its field. Elementary particles are considered point like, with no geometrical size so it is hard to describe what spin means without understanding quantum field theory.

Think of spin as a degree of freedom. In simple terms, it describes the symmetry of a particle. Let us pretend for a moment that point particles had shape. Let's further pretend that we could draw one. So, get a piece of paper jeffreyh and draw. Take a piece of rectangular paper, with equal length on each side and equal width on each side. Somewhere near the top, draw a star that is exactly center between the left and right sides, but higher than the center from top to bottom. Now, there is only one way to rotate this piece of paper to make it appear the same. A 360 degree rotation. This is spin 1. For a particle of spin 1 to be in the same state requires exactly a 360 degree rotation.

Now take another piece of paper. In the top left corner, 1 inch from the top and 1 inch from the left, put a star. At the bottom right, one inch from the bottom and one inch from the right, draw another star. Now, with a 180 degree rotation, the drawing appears the same. This is the symmetry of spin 2.

These particle obey Bose-Einstein statistics and are called Bosons. They are mathematically symetric during exchange of identical particles. Examples are the photon and the gluon. They are force carriers.

Strangely, a particle that obeys the Pauli Exclusion principle, in other words one of 1/2 spin, requires a 720 degree rotation to be in the same state. Two full rotations! Makes no sense in our macro world, but in the quantum world it is a fact. There is no analogy or drawing to explain it. We can mathematically describe it but it cannot be explained. In fact, all particles with half integer spins work this way. 1/2, 3/2 etc. They obey Fermii-Dirac statistics and are called fermions. They are considered mathematically antisymmetric. These are elementary particles. Examples are the electron, quarks and the muon. The spin does not change, only the orientation.

Quantum field theory does not describe a mathematical relationship between a particles spin and its charge. As far as we know, there is no correlation. Both charge and spin are inherent and fundamental, as far as we know.