I guess I can ask question #2, namely:
Why didn't Jesus tell them there was no such thing as ghosts as opposed to demonstrating why he was NOT a ghost.
I think the traditional evangelical position is that there are no ghosts because a person's spirit either goes directly to heaven or hell when they die.
But I recently re-read an account called "Blumhardt's Battle" about a humble German pastor in a small German town that had a multi-month spiritual battle, I.e. exorcism of a young woman in the town in the 1800s. The story is fascinating and pretty scary (she exhibited all the typical possession symptoms and some even more horrifying) but ultimately he discovered that it was not a demon that was inhabiting the girl but rather a "ghost" of a dead woman that had dabbled in black magic and murdered her children, and she told him she was cursed to roam in that state because of what she had done. Think "Marley" from A Christmas Carol.
The story is also told in a book called "the awakening". After the events of the exorcism, there was a major revival in the region, which this book tells about.
Both "Blumhardt's Battle" (which is Blumhardt's personal account) and "the awakening" used to be available to be read online but I don't think they are anymore. I really recommend them and the books can be purchased pretty cheap.