Your first question is a good one, in my opinion. I do not think that this is a particularly “Christian” question. The Bible will not help us to answer such a question! Science and philosophy are more appropriate here. I hope you will allow me to change the question, as I do not think that our “soul” does anything. The word soul, to be honest, is a bit hard to define. Let me change your question to “Do we act because of our brain or because of our conscious self/our will? Again, this is more of a philosophical than a religious question, but it is an interesting one. I think that the answer may very well be both!
First of all, we do not believe that mosquitos or alligators have a soul or a conscious self/will, yet they act. Alligators eat prey and mosquitos fly toward warm-blooded animals. Humans do acts which do not involve our conscious self. When I drive a car, almost none of the actions I take involve my conscious self or even the frontal lobe of my brain. I do not will myself to sneeze. Some human acts happen because of our brains. I do not believe that we can reasonably deny this.
However, there acts that we do that definitely do involve our conscious mind and our will. When I see a homeless person on the side of the road asking for food, it is not my brain that decides to stop and give the person some food. It is my will–my conscious self which makes this decision and does this act. Of course, pure determinists and, indeed, many atheists will deny the existence of human will and even of a self-aware person, but I believe that they are utterly wrong on that notion!
So, I hate to do this to you, but I say the answer is both.
On near death experiences, I have answered this a few times at the site already, but let me give you the really short version and I will let you do a search of the site for the term “near death experience”. Near death experiences give us no reliable information. There is good scientific evidence that there are physiological processes and brain processes which happen when our heart stops which could explain the kinds of out-of-body feelings and interesting “visions” that happen at such times. What people see is determined by their own pre-conceived notions of heaven and hell. Let us say for the sake of argument that some NDE’s really do reveal something real. How would we know which ones? NDE’s are an interesting category of experiences, but they provide literally zero reliable insight into the nature of life or life-after-death. Again, I will not absolutely deny that they might provide some information, but such information is too subjective and too unreliable to serve any real purpose.
No one can “prove” that life after death is real. What possible form could such proof take? Plato was one of the greatest thinkers and philosophers in all human history. He made some interesting logical/philosophical arguments about the afterlife in his famous dialogue Phaedon, where he argued for the immortality of the soul, but, no, he did not prove the afterlife is real. In case you are interested, Plato made four arguments for the immortality of the soul in the dialogue mentioned above. I am copying and pasting the four from wikipedia. Personally, I do not find these arguments particularly convincing. Personally, I believe in life after death because of the resurrection of Jesus and because the inspired Bible tells us that it is real.
- The Cyclical Argument, or Opposites Argument explains that Forms are eternal and unchanging, and as the soul always brings life, then it must not die, and is necessarily “imperishable”. As the body is mortal and is subject to physical death, the soul must be its indestructible opposite. Plato then suggests the analogy of fire and cold. If the form of cold is imperishable, and fire, its opposite, was within close proximity, it would have to withdraw intact as does the soul during death. This could be likened to the idea of the opposite charges of magnets.
- The Theory of Recollection explains that we possess some non-empirical knowledge (e.g. The Form of Equality) at birth, implying the soul existed before birth to carry that knowledge. Another account of the theory is found in Plato’s Meno, although in that case Socrates implies anamnesis (previous knowledge of everything) whereas he is not so bold in Phaedo.
- The Affinity Argument explains that invisible, immortal, and incorporeal things are different from visible, mortal, and corporeal things. Our soul is of the former, while our body is of the latter, so when our bodies die and decay, our soul will continue to live.
- The Argument from Form of Life, or The Final Argument explains that the Forms, incorporeal and static entities, are the cause of all things in the world, and all things participate in Forms. For example, beautiful things participate in the Form of Beauty; the number four participates in the Form of the Even, etc. The soul, by its very nature, participates in the Form of Life, which means the soul can never die.