Is it possible to communicate with our past, future, and parallel selves in the dream state? Are we already doing that?

This is possible and, in a sense, there is ongoing communication but it is via the influence of karma. The bending of time through the Law of Karma brings energy around again and again from parallel lifetimes to our present experience. This is perceived subliminally, not as a direct knowing what might be taking place in the other lifetimes that is of a compelling or urgent nature that could have consequences to even disrupt the current life in some way. Events will just conspire to bring that about without announcing the cause or origin of the energy setting things in motion. This is one of the challenges of the free will experiment. It is very demanding of humans to develop a deep understanding of how the universe works and all things that can govern their existence to gain control over them and find ways to heal when out of alignment. This is the most valuable of skills and can influence your future tremendously with an ability to bring healing to bear in a timely way. Most people are simply experiencing many, many consequences with no way to intervene or take any action capable of influencing things for the better. This is most unfortunate but typical of human life in an age of ignorance. People need to learn about karma and its vast reach and the reality of multiple lives running concurrently that send energies forward and back through time and add to the intensity of what is taking place in a positive or negative fashion. There is risk involved in communicating with the self in other timelines. In most cases, people will not have the wherewithal to be of assistance and may, in fact, confound things through an attempt to help that is lacking in insight and awareness of appropriate safeguards. That is best left to the higher self to attend to and to Source Creator and the angelic realm to bring healing help. Requests can be made and that is the virtue of the Lightworker Healing Protocol as this is built in, to reach across time in all directions to assist the self in an ongoing fashion for every circumstance, time, place, and soul extension functioning.