Understanding of class-AB currents
Is the transistor Q2 solely driven by the input? I think this as there is no other path for the base current.

You are only thinking about the DC (biasing currents) and yes, then the currents could (I am not saying that they always do) flow like you have drawn.

However the DC biasing is only one aspect of how this circuit works. The signals are small variations of this DC biasing current. So let's say that 10 mA is flowing out at Vi, if the signal causes that current to vary between 9 mA and 11 mA then on average there is still flowing 10 mA out of Vi. But the signal current is +/- 1 mA !!!

The current through R is your choice. What happens if you increase the DC current through R, what happens if you lower it? Think about the collector currents of the transistors as well.

Class AB means that for large signals part of the output stage will have no current (Ic = 0 A), what does that mean in relation to having a large or a small DC biasing current flowing through the transistors?