Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a]}$$
Since the rocket is halfway between the two trees at the moment the two explosions occur, flashes from the two explosions arrive at the rocket at the same time since the lightning is moving at the speed of light $c$. So, $\bf yes$, the light flashes reach the rocket pilot simultaneously.
$$\color{blue}{\bf [b]}$$
The situation is different from the student's point of view (frame of reference), he saw that the light of the explosion arrived at the rocket at the same time, but he saw the left explosion occur first and then the right one (since the rocket is moving to the right).
So, $\bf no$, the two explosions are $\bf not$ simultaneous in the student's reference frame.
