What is meant by body mind and the world is born simultaneously ...Buddha nature will never break apart. Do we die or is life eternal.
Buddha-Nature refers to the mind free from suffering or free from 'self-views'. Buddha-Nature is the pristine purity of clear-light-radiant mind.
'Death' does not occur to Buddha-Nature because Buddha-Nature does not have any ideas, thoughts or views of 'self'.
Try to realise the worries, fears & traumas about 'death' are all related to beliefs in 'self'.
When there is no belief in 'self', both internally & externally, there is no 'death'.
This is called 'The Deathless'.
To study the Buddha Way is to study the self. To study the self is to forget the self. To forget the self is to be actualized by myriad things. When actualized by myriad things, your body and mind as well as the bodies and minds of others drop away. No trace of enlightenment remains, and this no-trace continues endlessly.
As for 'body & mind', these are just elements of nature that form the natural world. Dogen, above, emphasises dropping way the false idea that various bodies & minds are 'myself' & 'other selves'.
If you take the 12 Links of Dependent Origination the mind and body is created due to consciousness. Mind and body is also known as the world because what we know about the world is the mental model that we have in our mind.
Whatever is born eventually dies. What ever that starts come to an end. So we have to die and life is not eternal. Everything that is conditioned or causality arisen is impermanent. Death is an eventual part of the process governed by causality or Dependent Origination (DO). As long as the wheel of DO spins there is birth and eventual old age and death.