In a blast furnace, iron is extracted from its ore hematite. The substances added in the blast furnace which undergo reaction are hematite, coke and limestone.
The coke, which is primarily carbon burns to form carbon dioxide
C + O2 --> CO2
The carbon dioxide reacts with excess carbon to form carbon monoxide
C + CO2 --> 2CO
Carbon monoxide is a reducing agent and reacts with the oxide of iron Fe2O3
Fe2O3 + CO --> 2Fe + 3CO2
The limestone that has been added, is decomposed to calcium oxide
CaCO3 --> CaO + CO2
Calcium oxide reacts with impurities, primarily silicon dioxide that is present in the iron ore to form CaSiO3
CaO + SiO2 --> CaSiO3
The resultant compound floats above the molten iron as slag which is extracted separately.
Iron produced in a blast furnace has a lot of carbon as impurity which makes its direct application difficult. The iron has to be treated further before it can be used to make products or iron or converted to steel.
The response to your questions are: Carbon is the element that displaces iron in the iron ore. Carbon is a non-metal.
Coke (solid carbon/carbonaceous material) is added into the blast furnance in the extraction of iron from its ore. A very exothermic reaction occurs between coke and oxygen (from hot air blown in from the bottom of the furnace which is preheated to 800 oC) to form carbon dioxide:
C (s) + O2 (g) --> CO2 (g)
Carbon dioxide reacts with more coke to form carbon monoxide:
CO2 (g) + C (s) --> 2CO (g)
Carbon monoxide is the main reducing agent in the extraction process. In the reduction of iron (III) oxide, the reducing agent is carbon monoxide:
Fe2O3 (s) + 3CO (g) --> 2Fe (l) + 3CO2 (g)
The pure, molten iron is then drained off at the base of the blast furnace.