Question

How is sodium extracted from its ore commercial commercially?

Answer 1

Sodium is extracted from it's ore by electrolysis of fused sodium chloride.

The process is usually carried out ia a special electrochemical cell called the downs cell. The interior is lined with graphite which serves as the anode, and there is also a steel cylindrical cathode immersed in the cell. Fused sodium chloride is inserted into the cell along with some calcium chloride to reduce the melting point of sodium chloride. Current is passed into the electrolyte and it dissociates. Chlorine gas is collected at the anode and channeled into a tank for storage. While molten sodium metal is collected at the cathode and also sent to tanks for cooling and storage.

Answer 2

Because hydrogen has a lower discharge potential than sodium.
If it  forms in aqueous solution it would immediately react with the water and produce NaOH.

Sodium is extracted by electrolysis (in the Downs Cell) of molten sodium chloride (in the presence of calcium chloride to ensure the mixture stays molten at a lower temperature.)