(1) The first thing you should do is draw a spacetime diagram.
Since light rays have speed c,
we have
and
For low velocities of the rocket, you can use the Newtonian equations of motion
to substitute for and . Finally expand and neglect terms of order and .
The rest of the assignment is just applying the results in section 6.4 of the lecture notes.
and 
. Finally expand and neglect terms of order 
and