When I use Meta Stack Overflow to ask and answer questions, I earn badges. I think it is a reward. So, is there also any plan for punishment? Is there any plan for creating new badges for seriously downvoted questions and answers?
We generally avoid creating badges that would encourage a negative behaviour such as posting a question that will get heavily downvoted.
So at the moment there are no plans to create a badge for having a post of yours downvoted a lot.
But, there is a badge for removing a downvoted post of your own: Peer Pressure.