@Asalsio
Much like what it was answered, he has a Persecutory delusions, a condition where he or she is convinced someone's after them. In his case, the professor's condition's worse due to his old age where he forgot the things he himself fabricated, causing him to have fake memories.
Touma...
@vangstampede
They probably used someplace that could keep the body temperature cooler so the body would be preserved (E.g: Freezer).
So after visiting 'Maya' at the caves, after leaving, these guys manages to dump the body there to make it like a 'mummy'.
When a person kills people because they're 'protector of justice' and believe by fake news, this isn't called justice anymore.
It's called 'Blind Justice'.
@bozz2 "Hello! We are here to sell a fresh corpse! How much do we get?"
^ You think anyone wouldn't want to say it/ chase them out/call the police if someone does that? XD