In the nuclear reactor of a power plant:

(a) How do control rods control the rate of fission?

(b) How is heat removed from the reactor core, and what use is made of this heat?

a) In Nuclear reactors control rods are stick down into the fuel to absorb neutrons, to slow the reaction down, or withdraw to speed the reaction up.

b) Heat is removed from the nuclear reactor core with the help of liquid sodium. It absorbs the heat and transfers it to the heat exchanger. Then, this heat is used for converting water into steam in the heat exchanger, which is later used to produce electricity by rotating a turbine and its shaft which is connected to a generator.