So 'vil' can also mean 'want'?
Yes, that is what it usually means. If you wanted to say 'I will not die' (just implying the future tense), you would rephrase the Danish sentence in order to avoid confusion, e.g. to: 'jeg kommer ikke til at dø'
I translated it as "I will not die, I will live!" and it was accepted.
In Danish there seems to be no difference in writing 'I want to' and 'I will'
What a weird statement