Short answers, pulled from the story.
A standard Roman legionary cohort consisted of 480 soldiers, made up of six centuries of 80 men each. The first cohort of a legion was an exception, holding 800 men across five double-strength centuries of 160 each.
The cohort replaced the maniple as the primary tactical unit of the Roman legion from the late second century BC onward. Maniples were smaller formations grouped by experience level, the hastati, principes, and triarii; cohorts combined those functions into a single, larger unit capable of independent operation.
A cohort was commanded by the pilus prior, the most senior of its six centurions. The centurions were ranked by title from hastatus posterior at the bottom to pilus prior at the top.
The contubernium was the smallest unit inside a Roman cohort, consisting of eight legionaries who shared a single A-frame tent. It was led by a decanus, typically the longest-serving soldier of the group, and was assigned one to two pack mules and one to two camp slaves.
The primus pilus, also called the primipilus, was the commander of the first century of the first cohort and the most senior centurion in the entire legion. He was eligible for promotion to praefectus castrorum, the camp prefect and third most senior officer in the legion.
According to Vegetius, a fourth-century Roman author, each century in a cohort was equipped with a scorpio, a small torsion-powered ballista, for a total of six per cohort. Each cohort also had one onager, a stone-throwing catapult transported fully assembled on ox-drawn carts.