How does taxation work in feudalism for the commoner , freeman and noble in england?
And in case of bad harvest what happened?
Broadly speaking, taxation and rent is organised in terms of service, either through the provision of labour, or in terms of supporting it through other, often monetary means.
While the common conception for medieval peasantry is that rent was provided most often in kind through food rents, this was not necessarily the case, or at least those rents did not come from the tenants fields directly. A good illustration is Domesday Book: each settlement in Domesday is assessed by its ploughlands and other available agricultural resources, divided between the lord's ploughlands, and the men's ploughlands. In any settlement, tenant farmers (villeins and villagers, smallholders and cottagers) would facilitate their rent by providing days of service on the lord's 'ploughlands'.
Significant debate exists over precisely how large a ploughland is, how it matches up with earlier Anglo-Saxon and contemporary land measurements such as sulungs, carucates and hides, and how precisely they were recorded by the scribes from Hundred to Hundred. Despite its reputation, Domesday is often anything but precise. It's often assumed that a 'ploughland' is roughly analogous with an Anglo-Saxon 'hide' at around 120 acres, although this could change significantly based on location and type of agriculture. An individual tenant household, dependant on status, is very unlikely to have worked an entire ploughland, but is more likely to have worked around 20-40 acres across multiple fields, and then supplied labour as rent on those ploughlands that directly supported the lord. At Siston, just outside Bristol, for example, there were 4 'men's ploughlands' which supported a population of some 18 households (very approximately 80 people), and then two lord's ploughlands which were worked directly to support the household of Roger of Berkely. Given that he was also receiving rents from 16 other settlements, largely around Bristol, then this would have assured a comfortable income.
These arrangements could change from settlement to settlement. At Bathwick outside of Bath, Somerset, 1 ploughland supported a population of 20 households, but there were 5 lord's ploughlands, worked in part by a substantial number of slave households. This shortfall of ploughlands was made up for by 50 acres of meadow and 120 acres of pasture supporting a large number of pigs and a considerable 350 sheep, farmed predominatly for the lucrative wool trade. These would have netted considerable income in terms of tax.
Taxation for lords could take many forms which, again often boiled down to service or comparable recompense. Many Anglo-Saxon charters bequeath land "free of taxation except the usual terms", the trimoda necessitas or three necessities of providing manpower to repair roads and bridges, maintain fortifications, and to serve in the fyrd militia. Especiallt post-Conquest, this military need in particular is replaced by an understanding that the lord provide a suitable amount to pay for the equivalent term of military service from professionals. A similar concept is found in the 'knight's fee', the requirement to provide (usually) 40 days of military service. This could be replaced by providing the funds for somebody else to undertake those 40 days on your behalf. Taxation in terms of Domesday is based primarily on what the lord himself directly benefits from in a settlement, be that ploughland, woodland, mills, or livestock, and an estimated monetary value for each. One interesting exception are the 'farms of one night' written about extensively by Pauline Stafford and Ryan Lavelle. Originally an Anglo-Saxon phenomenon, these are estates tied directly to royal vils and manors, which are expected to provide a specific food rent. These estates are specifically mandated to support the inherently itinerant nature of early medieval kingship, to actually provide 'one night's' worth of feasting to the king and his retinue as he processed through a given region.