1. I think ghosts (for want of a better word) are a fact of life (no pun intended - I mean it). However, I don't consider what is commonly termed the 'supernatural' to be supernatural at all, and I'm convinced it has no connection whatsoever to any of the myriad of religions the people of this earth follow. In my opinion the 'supernatural' is completely natural (albeit pretty scary at times) and is simply something that science, as yet, is unable to explain............ but given time, I think it will.
2. Too many to relate on here.
3. No it doesn't prove that an afterlife exists, but it indicates to me that physical death may not be the end of our existence.