What are valid targets for the spell and the copy? If I can only choose their creatures could I choose to redirect it nowhere as a roundabout counter or do I have to pick valid targets?
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The original instance of Dynacharge is controlled by your opponent, so the only valid targets are creatures that that player controls. You must target a creature they control; you cannot choose an invalid target or target nothing.
You control the copy of Dynacharge, so you may choose one of your creatures as a target for the copy. If there are no valid targets or if you choose not to change the target, the copy will be countered as it would resolve for having an illegal target. Rule 706.2 says:
And rule 706.10c says: