You'll draw only one card when a creature with more than one -1/-1 counter on it dies.

If a creature with a -1/-1 counter on it dies at the same time as The Scorpion God does, you'll draw a card. The same is true if The Scorpion God dies with a -1/-1 counter on it.

If this creature dies but leaves your graveyard before the next end step, it will remain in its new zone.

The "next end step" refers to the next end step that occurs, not the end step of the next turn. If this creature dies before a turn's end step (for example, during combat), it will be returned to its owner's hand at the beginning of that turn's end step.