Based on the title of the book itself, you could ask:
"Who or what is/are the arrow(s) of God?"
"The religion of Igboland had been around for generations. Why do you think Christianity was able to displace it so easily?"
"How do you think Achebe's own early childhood experiences with Christianity and other religions are reflected in Arrow of God?"
"What do you think is the role of revenge in the novel? Does that say anything about Igbo culture?"
"After reading the novel, what do you believe is a good and bad function of competition?"
"What does it mean to be a man in Igbo culture? Does that, in any way, reflect on how Igbo culture views and treats women?"
"How are race relations portrayed throughout the novel? Does race have any kind of influence on power shown in this novel?"