Short answers, pulled from the story.
The Army of the West was created by a decree on the 2nd of October 1793 and activated on the 6th of October when Jean Léchelle assumed command. It was formed by merging the Army of the Coasts of La Rochelle, the Army of Mayence, and part of the Army of the Coasts of Brest.
The infernal columns were 12 military detachments ordered by General Louis Marie Turreau starting on the 24th of January 1794. Commanding 80,000 soldiers, Turreau directed these columns to sweep the Vendée, confiscate crops, burn farms, and kill suspected rebels. Women and children were not spared, and the campaign was later condemned as one of the worst atrocities of the French Revolutionary period.
The War in the Vendée was triggered by two measures imposed by the French National Convention: mandatory conscription of young men and the requirement that priests swear an oath under the Civil Constitution of the Clergy. The great majority of priests in the region refused the oath, and the local population resented conscription, leading to full rebellion by April 1793.
The army cycled through multiple commanders in quick succession. Jean Léchelle was the first, from the 6th to the 27th of October 1793, followed by Alexis Chalbos, Jean Antoine Rossignol, François Séverin Marceau-Desgraviers, and Louis Marie Turreau, among others. Lazare Hoche commanded the army during its final phase before it was absorbed into the Army of the Coasts of the Ocean in January 1796.
Turreau was suspended from command on the 13th of May 1794 and later arrested after the fall of Robespierre. He argued at court-martial that he had only been following orders and was acquitted. He went on to command troops under the First French Empire and remained in favor with the Bourbon Restoration until his death in 1816.
The first Army of the West was absorbed on the 6th of January 1796 into the newly formed Army of the Coasts of the Ocean under Lazare Hoche, after a pacification agreement failed to hold and further campaigning was needed. It came back into existence on the 17th of January 1800 when the Army of England was renamed, and was finally suppressed on the 20th of May 1802.