It's not good to say that 1.51 km/sec is close enough to 1.49 km/sec. It's very wrong because it's greater than 1.5 km/sec (the speed at the surface). You should expect that the rocket slows down, that is, loses kinetic energy as its distance from the moon increases, that is, gains gravitational potential energy.
See the red for some of the corrections - the ripple effect is left for you to deal with. I get the books answer for the first question.