Short answers, pulled from the story.
A villa rustica was a Roman farmhouse or country villa that combined a family residence with a working agricultural section. It typically consisted of two parts: the pars urbana (main house) and the pars rustica (farm area), and could serve as the management centre of a large agricultural estate known as a latifundium.
A villa rustica was a working farmhouse that served as both a residence and a farm management centre. An otium villa was built purely for leisure and luxury, and was a much rarer type, typically located along the Bay of Naples.
A villa rustica was usually divided into the pars urbana, which was the main house for the landowner and his family, and the pars rustica, which was the farm working area. Separate structures often housed farm labourers, along with sheds and barns for animals and crops.
A latifundium was a large Roman agricultural estate. In some cases a villa rustica sat at the centre of one, functioning as the administrative hub from which the entire landholding was managed.
Surviving villae rusticae have been identified across many modern countries including the United Kingdom, Germany, France, Portugal, Italy, Bulgaria, Austria, Switzerland, Turkey, Bosnia-Herzegovina, Serbia, and Saarland. Notable examples include Lullingstone Roman Villa in England, Villa Boscoreale in Italy, and Roman Villa Borg in Germany.
Germany and the United Kingdom have among the highest concentrations of identified villa rustica sites. Germany has examples spread across Baden-Württemberg, Bavaria, Hesse, Northrhine-Westphalia, Rhineland-Palatinate, and Saarland. The United Kingdom has more than a dozen named sites, including Chedworth Roman Villa, Fishbourne Roman Palace, and Woodchester Roman Villa.