Ghosts and the Supernatural
A 1: The length of your submitted query necessitated shortening it to the specific question above. You use as a basis for your question an experience that your neighbor claims of seeing the ghost of a 6 year-old girl. Your neighbor also claims that the ghost spoke to her and said all she wants is a mom. From that you ask what the Catholic Church has to say about ghosts.
The simple answer, albeit perhaps unsatisfactory, is that we do not believe in ghosts. It is fundamental to our belief that when we die, we rise to new life and enter the fullness of the kingdom. The notion of a spirit roaming about the world until some kind of life experience is satisfied is not consistent with that belief. Specifically in the case of your neighbor, a child who has died no longer has need of a mom. Perhaps this says more about your neighbor than it does about ghosts.In your question you state that your neighbor is credible and not a "psycho". I don't think those are the only possibilities. There is much about the human mind we still do not know or comprehend. Scientists are continually learning more about the powers of the brain. It may be that some experience in your neighbor's life has been left unsatisfied, and this experience is a subconscious attempt to resolve it. Or it may be that she has been influenced by some other factor. I do not pretend to know what is going on, other than to assert that I do not believe the ghost of a little girl is haunting her.
A 2: First, let's deal with purgatory. As you suggest, the notion of purgatory as formerly taught, namely, that people live in an annex of heaven (or hell) until they have been purged and are ready to enter heaven is not a very helpful or satisfactory idea. Perhaps a better way to understand purgatory would be to suggest that the very death experience is itself purgation. Death, no matter what kind, is the most violent disruption of human life. Even for those of us who believe in a resurrection, there is no proof that we rise to new life. Everything we have known and experienced, everything that we are comes to an end with death--at least from an earthly point of view. That great disruption of life can be seen as purgation, a purification that prepares us for entrance into heaven. Ultimately we are transformed, and hence purged, by God's love. God's love is working a continual transformation in our lives. Our own imperfection and sinfulness make it at times more or less effective or difficult to see. At the time of our death, we can no longer make decisions that resist God's love. At the time of our death, God's love has the final word. We are perfected by that love and enter into the fullness of the kingdom.Secondly, this idea of God's love is the whole foundation of salvation. If, at the time of death, it is God's perfect love that prepares us to enter heaven, then the idea of ghosts is incompatible with salvation. In the same way, the idea of evil spirits as those who are not ready to enter into heaven is also incompatible.
A 3: My response to the first ghost question answers the query about Ouija boards. What is different about this question if the issue of exorcisms.
There is no requirement for Catholics to believe in demonic possession or exorcisms. And, in fact, many Catholics today find the idea more than a little embarrassing. Clearly, there is evil in our world. Even if someone chooses to believe in a personified evil called Satan or devil (and I do not), it is quite another thing to believe that God would allow that evil to possess a human person. I cannot find a way to harmonize that thinking with an all-loving and good God.