Glad to weigh in on it as I read the book earlier this year. There are many wrinkles to Karamazov, and I could really only begin to scratch the surface but here are some thoughts.
To your question of the tavern scene and the need to be virtuous. I am not sure that this is even a settled debate amongst Christians. For example many Protestants tend toward the doctrine of “salvation through faith alone” while it is an older and more Catholic framing of the issue to say that salvation is tied to acts. Still others claim it is a semantic argument and that Christians are saved by their acceptance of Christ and simultaneously are called to good deeds thereafter.
Now as for Ivan’s assertion about immortality of the soul being bound to the concept of virtue, I am not sure I can agree with this either. Few if any persons on earth would agree with his conclusion that “all things are permitted” just because immortality is taken off the table. This is something of a reference to the Hobbesean “Natural Law” issues, in which Hobbes and other philosophers posit that man forfeits his “right to all things” in a bargain with other men, to preserve his own most basic of rights from being violated.
I think there is significant material of interest here for anyone to ponder, regardless of their religious belief or lack thereof. I will also say however that Dostoyevsky’s major works, taken together, are a powerful argument for Christianity. Specifically Brothers Karamazov and Crime and Punishment seem to elucidate a set of values that can be appreciated by the irreligious, but also stand in strong contrast to the secular self-justifications that were predominant in the time and place Dostoyevsky wrote.