Flywheel/Dynamo behavior under variable load
what is the behaviour of a flywheel/dynamo system in relation to the
electrical load being served?

Assuming 100% power efficiency in the dynamo, whatever electrical power is being removed from the dynamo to drive an electrical load is seen as a mechanical power burden on the flywheel and that of course will gradually slow down the flywheel.
That mechanical power burden equals the electrical power taken from the dynamo and, as the speed slows, if the electrical power take-off remains constant then more load torque is felt by the flywheel and this might rapidly bring it to a halt.

What force does the rotor experience as a result of the dynamo's
presence?

$$\text{Power} = 2\pi n T$$
Where T is torque and n is the revolutions per second of the rotor. So, the force it experiences is a torque proportional to the electrical take off power (plus mechanical losses).

Does that change as the load changes?

It has to change else you would have free energy for nothing.