Which was the first nation to field a national professional army?

Answer 1

Early armies were either those of nomadic or agricultural societies, and so comprised the general manpower of the tribe/people/citizens fighting for territory, loot or defending their farm or territory.

Possibly the first to rely mainly on mercenary troops was Carthage. At Agrigentum in Sicily in 480 BCE, it lost the flower of its young men who were ambushed and wiped out crossing a river, and thereafter determined not to expose its citizens again. They were great traders and could afford to hire other peoples to crew their warships and fight in their land forces.

Afternote: When Rome defeated Carthage in the Second Punic War in 203 BCE, it realised this link, and imposed a severe financial indemnity designed to cripple Carthage's ability to hire mercenaries for 50 years. The Carthaginians were such good traders that they paid off the debt in ten years, and so, in Roman eyes, returned to being a threat to Rome. Then followed a pattern of Roman-organised harrassment of Carthage, using client North African kings as proxies, and eventually the final conquest by Rome in the Third Punic War with the city's total destruction and sale of the people into slavery.