Under the manorial system, the medieval system for which western Europe is best remembered, farmers did not usually own the land they farmed. Most of them were usually serfs or tenant farmers, the difference being that the serfs were not entirely free and could not move off the manors where they worked, but the tenant farmers could. There were other farmers, however, who had their own small holdings, and these people were called yeomen.
There were other systems in use as well, in addition to the manorial system. It was not used in the Byzantine Empire, and other parts of Europe, including Scandinavia and Russia. And it was not used for the entire Middle Ages. So generalizations are never entirely accurate.
I think the king gave the lords the land to do what they wanted, and the dukes got the land from the lords to give to other people if they wanted, or to keep.
The political scene in Medieval Europe was most characterized by the Feudal system. The Feudal system involves a very loose collection of lords and vassals who control their own plots of land and laborers, but pledge their loyalty to a single king. By nature, the feudal system is very decentralized as the day-to-day decisions were made by the individual lords and vassals over their individual areas of land, and were not decided by a king holding central authority.
Travel was by foot for the residents of a village. The Lord of the Manor would be the only one with access to horses. Some of the villagers and local farmers would travel to neighbhouring villages on market days for trade, but travel generally was limited. This is how local accents came about in places like the UK. Each village had their own form of the language because of the isolation.
Actually, they did bathe in the Middle Ages. The people believed that cleanliness was next to godliness and kept very clean. They also believed that bad air, with foul odors, carried diseases. They had public baths in many villages. Later, the Renaissance came. People discovered perfume and went into a period when the only parts of the body to get cleaned were the parts other people could see. They knew medieval people did not have perfume, and liked very much to describe the Middle Ages as inferior to their own, so they called the medieval people dirty and stinky. They convinced alter historians of their own superiority, and people still believe them.
Most serfs lived on manors. These were farming estates that belonged to lords, and whose residents were mostly serfs. The serfs typically lived in a village or hamlet on the manor, in cottages. Some serfs were not agricultural and worked as laborers. They typically lived in cottages in villages or boarding houses in towns.