It's futile to argue about definitions. All you can really say is that one is more or less useful than another. What is the utility of defining nihilism in a way that makes it consistent with belief in something? The real problem is the concept that a Christian could be an existential nihilist, which you've defined as "the belief that life has no ultimate purpose or meaning". Most Christian existentialists (like me) make the "leap of faith" that there is an ultimate purpose or meaning to life.
Probably not, because that would involve a definite value system--e.g., the one at Jonestown. As a practical matter, people who have that point of view are at a real evolutionary disadvantage and don't make much of a mark on history. Martyrdom is a special case, and is never done because of nihilism, quite the opposite. But as one of my Muslim friends says: you don't see many suicide bombers over thirty. They're just going through a phase.
I agree, persons should not wager their lives on the ideological obsessions of old men and their scribblings.