I would prefer to die than ... is an odd thing to say because 'prefer' means 'like more'. It is connected bro enjoyment or pleasure. It's strange to say that you would like to die. It's strange bro say that you would like to die more than you would like to do another thing.

'I would rather die than . .' is not to be taken literally, unlike 'I would prefer . .' It's a statement of your strong feeling about something. In general though the two expressions 'I would rather . .' and 'I would prefer . .' are equivalent and interchangeable.

No, "would rather" cannot always be replaced with "would prefer." In your example, "I would rather die than apologize to him" conveys a strong, dramatic choice, emphasizing personal feelings or principles. If you replaced it with "I would prefer to die than apologize to him," it would sound awkward and less natural because "prefer" is typically used for more measured or practical comparisons, not extreme or emotional situations. For dramatic statements like this, "would rather" is the better choice.