Submit C# MapReduce Job Windows Azure HDInsight - Response status code does not indicate success: 500 (Server Error)
I had approximately same issue in the past (was unable to submit hive job to the cluster with BadGateway response). I have contacted the support team and in my case the problem was in memory leakage at the head node, what means that the problem was not at client's side and it seems to be inherited hadoop problem.
I've solved that stuff by redeploying the cluster. Have you tried to submit other jobs (simple ones)? If so, than I suggest to have a contact with azure support team or just redeploy the cluster if it's not painful for you.