Short answers, pulled from the story.
Infantry are soldiers who specialise in ground combat, typically fighting dismounted on foot. The term entered English around the 1570s, travelling from Middle French infanterie and older Italian and Spanish infanteria, meaning foot soldiers too inexperienced for cavalry. It traces back to the Latin word for newborn, speechless, or foolish, the same root that gives English the word infant.
The individual-soldier term infantryman was not coined until 1837. The broader term infantry had already been in use since about the 1570s. Some forces, such as the Canadian Army, use the word infanteer instead of infantryman to name a single soldier of the infantry.
Motorised infantry ride trucks and other unarmed vehicles for movement but leave them to fight on foot. Mechanised infantry use armoured personnel carriers that allow at least some combat without dismounting. Some of these carriers became infantry fighting vehicles, with combat abilities approaching those of light tanks.
In the late Roman Republic, legionaries earned the nickname Marius' mules because their main activity seemed to be carrying the weight of their legion on their backs. The practice actually predates Gaius Marius, the man it was named for. Such heavy infantry burdens have changed little across centuries of warfare.
The first known organisation of military forces into regular units appears in Egyptian records of the Battle of Kadesh, around 1274 BC. Soldiers were grouped into units of 50, then 250, then 1,000, and finally into units of up to 5,000, the largest independent command. Similar layered ratios of roughly 10 to 100 to 1,000 appear in other ancient armies.
As firearms improved, armour had to be made thicker and heavier, which hindered mobility. The heavy arquebus, built to pierce standard steel armour, showed it was easier to make heavier firearms than heavier armour, so armour shrank to close-combat use and then largely disappeared. Helmets returned during World War I to guard against artillery fragmentation and blast, and composite materials like kevlar have since begun a return to body armour.