Do electrons move faster than the sped of light?

No. Since they have mass then they cannot reach the speed of light, let alone exceed it.

Mass and energy cannot move faster than light; and only energy, e.g., photons, can actually attain (but not exceed) light speed. Mass, in the form of protons used in colliders, have been accelerated to about 99.9999991% light speed, but that's all the faster even the most powerful colliders in the world can get them to go.

Here's why.

The invariant rest mass, normal mass like you and me (and my dog Boots), takes on additional inertia as it speeds up. And as we know from Newton's First, more inertia means more force (energy) is needed to change speed and/or direction. There comes a point where the speed has raised the inertia to a point where there simply is insufficient energy to change the speed and/or direction one iota more. And that point shows up below the speed of light.

All this is covered in the special theory of relativity by Einstein.

Well.... Since electrons can move from one energy level to a different energy level without ever having an energy in between, if different energy means different physical location, then electrons may exceed the speed of light. However... there are a whole lot of things about electrons that defy conventional understanding. First and foremost, they will behave like a particle and then they will behave like a wave.

I believe it was Albert Einstein who said: if you can't explain something to a 5 year old, maybe you don't understand it very well. I think this applies in spades to quantum mechanics.