1. In an environment such as this EvC forum, should a participant be required to answer relevant questions? For example, what is your definition of evolution?
No. But it demonstrates poor etiquette if the person can't even address a legitimate question.
2. I hold that if a participant does not answer, they are being unethical. Do you agree or disagree?
If the person was responding to other questions prior to this, then I agree.
At the very least he/she is guilty of rude behavior.
3. If a participant behaves in an unethical manner and yet continues to participate, are they being dishonest? Obviously, I say yes.
No, but they are certainly being rude and demonstrating they don't really want to discuss the topic, just jabber away broadcasting their own thoughts.