Greeting classmates!
In response to the first question, "Which of the reasons for needing a process of interpretation is the most compelling or helpful for understanding the Bible?" my response would center on that we have a tendency to insert our own questions or perspectives onto Biblical interpretation. Here is why I see this being the most compelling reason for a process - the perspectives of fallen children CAN be dangerous! Let's face it, we get things wrong ( a lot). Relying on our own, narrow view, of God's expansive word limits God to our own experiences. It can reduce Him to things like a "cosmic genie" or an "irritated dad". I process of Biblical interpretation allows us to maximize our limited world-view of scripture to ensure that we have the Best chance to get things accurate!
I have not heard it called the Fourfold Approach but I have seen this approach in action. A colleague named Misha has introduced me to this way of looking at scripture in the past as I began sermon prepping 1/2 year ago. I had not thought prior to ask the question "what obstacles exist that need to be overcome to make the scripture relevant today?" I like that and plan to add that to my studies!
I think the aspect of context I see most often ignored is "original context" and I believe it is because it requires further study into history, geography and culture. Perhaps when the context requires additional study people might not be inclined to pour forth extra work! I find original context fascinating although the different language translations of words and meanings tends to get a bit dense for me...