Short answers, pulled from the story.
A battle is well defined in duration, area, and force commitment, whereas a skirmish involves only limited commitment between forces and produces no decisive results. When a battle lasts longer than a week, military planners often reclassify it as an operation.
The word battle is a loanword from the Old French bataille, first attested in 1297, derived from the Late Latin battualia, meaning the exercise of soldiers and gladiators in fighting and fencing. The English word battery shares the same Latin root, battuere, meaning to beat.
A Pyrrhic victory is a battle outcome that formally favors the winning side but ultimately benefits the defeated party. The Battle of Asculum is a historical example: the winning side suffered such losses that it was compelled to reconsider its strategic goals.
Battles are usually named after a nearby geographic feature such as a town, forest, or river, prefixed with the words Battle of. After Henry V defeated a French army on the 25th of October 1415, he met with the senior French herald and they agreed to name the engagement the Battle of Agincourt after a nearby castle. In desert warfare with no nearby landmark, map coordinates have supplied the name, as with the Battle of 73 Easting in the First Gulf War.
The Battle of Megiddo, fought in the fifteenth century BC, is the first reliably documented battle in history. Unlike the unorganized crowd combat that preceded it, both armies at Megiddo were organised and disciplined.
Battles are decided by the number and quality of combatants, the quality of weapons and armour, the skill of commanders, and terrain. Superior weapons can be decisive, as at the Battle of Omdurman, where Maxim machine guns and artillery destroyed a traditionally armed force. Disciplined troops also matter greatly; at the Battle of Alesia, the Romans were greatly outnumbered but won through superior training.