I don’t think it’s really spirit but more like questions about the self and the body. I know that “no self” is a common element in eastern philosophy so their view on death is different. Since there is no “you” nothing really does but is more like transmuted (I think). It’s similar to how energy can’t be created or destroyed but transferred from one form to another.
But you wouldn’t really be reborn because once you die that body is not “you” any more.
Nah, they believe in “spirit” or “soul” that is not very different from the western concept.
No self is a big misconception of Buddhism, especially by western atheists. Buddhists believe that “self” exists but its something to be overcome in order to reach enlightenment.