You ask "Does the wave function/density state actually exist?" but this is a question that can't be answered. Quantum Mechanics is a mathematical model that gives an excellent description of the real world. QM is based upon the assumption that the wf/ds is a real object, but whether QM is a "real" description of the world is a question we need to leave to the philosophers.
In a comment to another question, Is there a mechanism for time symmetry breaking?Is there a mechanism for time symmetry breaking?, someone mentioned this paper. Although I'm not sure it revolutionises our understanding of the wavefunction it makes an interesting read in the context of this question.