How does the sun move over the year in the sky of the Moon? Wikipedia's section on the Moon's inclination says it is always 1.5&deg; to the ecliptic. Does that mean that as seen from its surface, over the year the sun at zenith would move 1.5&deg; to the north, then to the south, varying by 3&deg; overall?
That's right. Unlike the Earth, which has a substantial inclination of 23.4 degrees to the ecliptic, the Moon is inclined by only 1.5 degrees. This means that there are no substantial seasons. The moon also spins much more slowly than the Earth. Each "day" lasts for one Earth month. It also means that at the poles there are craters that are completely shaded from the sun. In these craters, there may be useful amounts of water ice.

Now as noted by the Wikipedia site, this is due to two motions being linked. The moon's orbit is inclined by 5.1 degrees to the ecliptic, and the moon's equator is inclined by 6.7 degrees to its orbit, however the direction of the pole moves to keep these two angles always in opposite directions to each other (There can be no pole star on the moon) The result is that the inclination of the moon to the ecliptic is fixed at 1.5 degrees.