Process heat and electricity generation.
The very first nuclear reactor was Chicago Pile 1. It was built for research and scientific use. The first nuclear reactor outside of a university was built (at Hanford, Washington) primarily to yield plutonium for the atomic bomb destined for Nagasaki, Japan. Nuclear reactors were built primarily for electrical generation beginning in about 1951.
Stabilise the arc and optimize the operation of the furnace.
No. A nuclear weapon requires a critical amount of highly enriched fuel to be rapidly brought together to cause a sudden explosion. Nuclear plants use low enriched fuel which could never cause a nuclear explosion, and this fuel is dispersed through the reactor in any case so it could not suddenly come together. Any nuclear plant explosions (like Chernobyl) are caused by the presence of high pressure steam and water circuits, not the fact of it being a nuclear plant, though certainly if there is an explosion of a pressure circuit and hence a loss of coolant, and disruption of the nuclear reactor, radioactivity may escape from the plant. This is the chief preoccupation of designers and operators, to keep the plant safe and prevent this ever happening.
Only electricity production
By Reactor I assume you mean a thermonuclear reactor. Most thermonuclear reactors use Boron rods to absorb radiation. This prevents the chain reaction in the reactor (where uranium nuclei split, each split nuclei further colliding and splitting more nuclei). They steam systems (that drive the turbines) are usually heated by gas or water. That is what the big towers are - cooling towers. The water is pumped to the top of the tower, and allowed to fall under gravity. this provides contact with the air and has a similar effect to sweating. If gas cooling is used, large radiators (like those on a fridge) use convection currents to move heat away from the reactor.
A breeder reactor is one type of nuclear reactor, but not a type that is in general commercial use at the present time
the nuclear reactor exploded
It would be used as a more efficient version of a Nuclear Reactor. While a regular nuclear reactor requires almost a factor of 100 greater in fuel amounts, a Breeder reactor uses much less and produces less waste.
No, a nuclear reactor cannot detonate like a nuclear bomb. Nuclear reactors use controlled fission reactions to generate heat for electricity, while nuclear bombs use uncontrolled chain reactions to create an explosion. The design and purpose of a reactor prevent it from causing a nuclear explosion.
That released by fission in a nuclear reactor
To produce electricity
No. LLNL even tested several Uranium-Hydride bombs in the 1950s. Even though their computer models said the devices should explode, none gave a nuclear yield. One could use the waste from the reactor as a Radiological Weapon, but the reactor itself is not useful as a weapon.
If you are a smart guy, you can make a nuclear bomb, or a nuclear reactor...
A nuclear reactor will do what is asked here. Use the link below to the related question about what a nuclear reactor is.
Heat is eliminated through use of reactor coolant passing over the nuclear fuel in the primary coolant loops.
not practical
A neutron reflector enhances the efficiency of a nuclear reactor by reflecting neutrons back into the reactor core, increasing the likelihood of nuclear reactions and the production of energy. This helps sustain the chain reaction and improve the overall performance of the reactor.