(a) In the electrolytic reduction of alumina, the graphite (anode) is oxidized by oxygen to CO and further forms CO2, so it is consumed and has to be replaced from time to time.
2C + O2 ⟶2CO
2CO + O2⟶2CO2
(b) Roasting provides oxygen to convert metallic sulphides into metallic oxide and SO2 which takes place when heated in excess of air.
Carbonate is converted into oxide by loss of CO2 which takes place in the absence of air and when heated strongly.
(c) Aluminium has a great affinity towards oxygen and so cannot be reduced by carbon or carbon monoxide or hydrogen whereas lead oxide can be easily reduced to metal lead by carbon.
PbO + C ⟶ Pb + CO