Background: I'm a CS grad student. I've taken a course on computational complexity.
Can you suggest an introductory book on quantum computation, especially regarding the details of Question 2.
Argue whether it's hard to separate $QIP[i]$ from $QIP[i + 1]$ for $i < 3$. I know $QIP$ collapses to $QIP$. The simple argument is that this question is hard because we still can't separate P from $PSPACE$. Note $P \subseteq BQP = QIP$ and $PSPACE = IP = QIP = QIP$. However on the other hand, I would think separating $QIP[i]$ from $QIP[i + 1]$ is easy, because the difference is obvious. The only thing left to do is to define a language that exploits the difference.
Remark. To me question 1 is more important than question 2. :p