You are going to have to be a tough cookie.
When you receive a task from her, get back to your desk and review the task that she has assigned you. If you have questions to ask, make a list of questions, then make an appointment with her to go over the task before you start on it. Before you get to her desk, make sure that your mental attitude has reached the point where you don't care that she screams at you. Mind over matter. You don't mind and she doesn't matter (*). On the other hand, you need those answers and those answers are all you need her for.
When you are with her, go through each question until you are satisfied that she has answered your questions. Every question. If some of her answers raise more questions, that's too bad for her. Think "noise to signal" ratio. Her screaming is noise and you don't care about noise. You can hear it but ignore it. All you care about is "signal", which you getting the information you need to perform your task. I have ignored bosses who were screaming at me 30 cm or 1 foot away from my face, so I know it can be done and that my advice is not idle advice. All you need is practice :)
Don't let any of her screaming get to your head, even though it's ringing in your ears. Shut down the ear to brain connection while she is screaming at you, filtering only for the information you need. Don't take her screaming personally: apparently, from your mention that she is sort-tempered with people at and above her rank, I'd say that she treats everyone she thinks is incompetent the same way - like dirt. You need to be confident in your abilities in dealing with her. I sense that she respects competence and intelligence but that she is all too quick to wrongly assign incompetence and stupidity. In dealing with her, never be ashamed or act ashamed of any gap in your knowledge. Ask your questions up front. The more of your questions she answers, the less pain you have to deal with going forward as you get closer and closer to fully figuring out her approach to analysis.
If her screaming nonetheless gets to you, stare at her icily and say "LOOK! I am not a mind reader and the only way I know what you want is when I ask you want you want and you give me an answer." Pay attention to your body language and your demeanor: don't be a mouse when you are meeting with the cat. In fact, you don't even want to be seen as a mouse, given what cats do to mice.
Make sure that you have a conversation with your manager's boss about your manager. Let your manager's boss that the relief you seek is that that her screaming stop. Apparently, there is some kind of consensus among the rank and file of the firm that her interpersonal approach is in conflict with the firm's culture.
(*) If a tree falls in the forest and no one sees it fall, does it matter? If she screams at you 30 cm or 1 foot from your face and you just don't care, does it matter?