Do charges (static or moving) reflect light? If no, then how can we see a spark?
A spark emits light, it doesn't have to reflect it to be seen.
Free charges indeed reflect light, and quite well. Look at a mirror - it is free electrons which reflect.
Charges also emit very well when they move with acceleration. That is why we see a spark, a flame, Sun, etc.
And what makes spark to emit light?
The spark heats up the air to tremendous temperatures (into a plasma), which then emit their energy as light.
Atoms are electric charges, right? Right. They have electric field around them. When you shake an atom (say, atom is fast thermal motion in a spark), then field begin to shake too. This shaking electric field is what we call "light".
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