Dealing with work bullies is no different than how we teach our kids to deal with playground bullies - you stand up to them and don't let them feel like they can walk all over you. If and when he sends these bolded, loud, obnoxious messages you reply all with bolded, loud, obnoxious messages right back at him with explanations why he is wrong. Then you follow that up with a trip over to his desk asking him directly to his face why he feel the need to blast you publicly like that without the facts. These sorts of responses will make him think twice about doing it again. These bully-types feed off of people they think are weak so don't give him that impression, push back and push back hard.

One thing I would NOT do is answer him right away. In my experience, people like him want immediate responses and will email you incessantly to get it. They will escalate. Let him. Let him hang himself. For example, when he asks the status, wait 15-20 minutes (whatever would be acceptable in your group) and answer him briefly and without explanation. For example, he says "why didn't Bob complete this report?" I would never explain Bob's actions. I would say, "the report is expected to be completed on ." and let it go. The more information he has, the more ammunition he has. He will bombard you. Let him. Then keep copies of his emails, notes about his responses and go to your boss or HR and express your concerns about Bob: he seems stressed, he's sending so many emails that he isn't meeting his own targets, he's interfering with others doing their jobs, etc. Overall, you can't change him. But you can manage him. You can also have boundaries. Ultimately, if you can't stand working for him, you can try to change positions/jobs.