After reading book two, my impression of the characters was pretty much the same. Ivan still confuses me: earlier in the book he was called an atheist, but in his arguement with the monks and Misuov he claimed that the state should become part of the church.
The plot is finally beginning to develop. There is a love triangle between the family members: Dmitry is engaged to Katrina, but likes Grushenka, whom his father also likes, and Ivan likes Katrina. Also, there has been hints that a murder will occur (that of Fyodor) and the elder bowed in front of Dmitry, and Ratikin said it was because he was predicting Dmitry was going to be the murderer.
The author is hinting at a theme of finding an answer to "the problem inside your heart," as the elder told Ivan.
I have to say, I didn't understand some parts of the arguement between Ivan and the monks.