"Die of X" Using the word 'of' implies something from a set of several possible things caused it. eg: "He died of starvation." Using 'of' implies that starvation is one of many things that could have killed him - imagine a list of possible causes of death, like sickness, age, etc. Using 'of' specifies starvation as that cause. "Even though they were fed, they died of frostbite." "The astronaut died of suffocation." "Die from X" Using 'from' implies a specific cause, which is referred to. eg: "He died from his wounds." The wounds are specifically the thing that killed him. "The harsh winter caused them to die from cold." Again, in this case, the harsh winter is what killed them. "Despite being warm, the lack of medical supplies caused them to die from disease." Even here, using 'of' would make sense too. Overall, there isn't a huge difference between these two cases, and using either word would make sense. However, there are certain cases in which you really should use one or the other: eg. "The soldier, who had been shot, died of his wounds." This sounds really bad, even though everyone would understand it. Using 'from' would sound a lot better, as we already know the cause of death (being shot). Hope this helps, it's my first time helping out here :)

I would say there's a subtle difference. A person might die of a sickness or a natural cause, (die of cancer, ...a heart attack, ... old age) Or, a person might die from an accident or at the hands of a person/animal, (die from a car crash, ...falling off a ladder, ...gunshot, ...bear attack) I think the two terms are basically interchangeable, but the examples above may be a bit more commonly used.

I don't believe there is a difference. For example "going to the park" and "On my way to park". I can see how the difference could be subtle depending on the context of the sentence.