Just a couple of things. Firstly I think it's easiest to visualize (by drawing a diagram with the moon/centre/radiis etc) what's going on so you can intuitively work out stuff. Secondly you need to assume that the acceleration due to gravity at the Moon's surface is for both parts of the question. Thirdly you need to assume that the acceleration due to gravity at a point outside the Moon is inversely proportional to the square of the distance from the centre of the Moon i.e.
Sorry don't know how to put space in the text, so here's a link to a picture of it mechanics q.png