Shielding is used to prevent the escape of neutrons from a reactor. A moderator is used in the reactor to undergo collisions with a neutron. The neutrons produced in fission collide with the molecules of the moderator, imparting their kinetic energy on them. This generates heat in the reactor. (Temperature is the measure of the average random molecular kinetic energy of a substance).

efficient coolant that does not act as a neutron moderator.

The primary role of graphite moderator is to moderate the neutron energies however it may also capture some heat during reactor operation.

Moderator is not used in case of fast breeder reactor because there is no need to slow down neutron energy. Nuclear fission takes place at high energy of neutrons.

The neutrons released from Uranium are fast neutrons. In a reactor they are slowed down by a moderator. The moderator could be water, heavy water, graphite, among others. When the neutron is slowed down, it is more likely to create fission.This is what happens with the U-235. The U-238 does not fission, but it does transmute through a series of neutron absorption and beta decay etc. into plutonium which does fission also.