"can a wiki admin ban users arbitrarily, or are they required to provide a reason"
Since the new blocking policy, the blocking user must provide either a rule that has been broken, or provide a reasonable summary, such as "User has been proven to be underage: (proof)".
"If they are required to provide a reason, can the reason be arbitrary, such as 'I don't like this guy'"
A lazy reason like "I don't like this guy" is surely unacceptable.
"If the reason can't be arbitrary, can they make up lies such as ' this guy is a dupe of mr. X '"
Of course not, that is unacceptable too.
"I basically want to know if wiki admins are dictators, or can they be demoted for power abuse"
For more information, read the new blocking policy. If you have any other question, contact FANDOM staff through their support channel, not their message walls: https://fandom.zendesk.com/hc/en-us/requests/new?ticket_form_id=360000940393