Demure and demur: Demure is an adjective meaning modest and shy, perhaps to the point of primness. Demur is a verb meaning to object and is so archaic that you probably shouldn't use it, except to know that it's not the same as demure.
Appraise and apprise: To appraise is to size up or estimate, as in value. A jeweler appraises a ring. To apprise is to inform or give notice, as you would apprise someone of a change.
And here's a little shout-out to writers of paranormal non-fiction: Having a glossary at the end of your book does not give you the right to change the definitions of words to suit your agenda.
