Short answers, pulled from the story.
The distinction between a hill and a mountain is unclear and largely subjective, but a hill is universally considered not as tall or as steep as a mountain. Geographers historically regarded mountains as hills greater than 1000 ft above sea level, while hillwalkers and the Oxford English Dictionary lean toward a 2000 ft limit.
In the UK and Ireland a mountain is usually defined as any summit at least 2,000 ft high. The UK government's Countryside and Rights of Way Act 2000 separately defined mountainous areas for open access as areas above 600 m.
Hills form through geomorphic processes including faulting, erosion of larger landforms such as mountains, and the movement and deposition of sediment by glaciers, which creates moraines and drumlins. Their rounded peaks result from downhill creep, the slow diffusive movement of soil and regolith down the slope.
Many settlements were built on hills to avoid floods, for defense through an elevated view that forced attackers uphill, and to avoid densely forested areas. Ancient Rome was built on seven hills, which helped protect it from invaders.
Hills give an army that controls their heights an elevated view, a firing position, and the advantage of forcing opponents to charge uphill, and they can also conceal forces lying in wait on the crest. Because of this tactical value, hills were the site of battles including the Battle of Alesia in 52 BC, the 1775 Battle of Bunker Hill, and the Battle of San Juan Hill in the 1898 Spanish-American War.
Hillwalking is a British English term for hiking that involves the ascent of hills, distinguished from mountaineering because it does not require ropes or technically difficult rock climbing. Munro bagging is the activity of climbing the hills on the Munros list of Scotland, with the aim of eventually climbing every hill on the list.
Sophienhöhe in Germany is the tallest listed artificial mound at 200 m. Other notable artificial hills include Monte Kaolino in Germany at 120 m and Kvarntorpshögen in Sweden at 100 m.