I know that under a feudal system, all land was really owned by the king, who granted the rights to manage it to lords, who in turn further divided it to people that actually worked the land.
But once a lord had been granted these rights, was it basically theirs to do with as they wish? Could they sell or trade the whole or parts of it freely, or did that require permission from their king?
Could (theoretically) essentially anyone buy the rights to the land from a lord, and become vassal directly under the king, without the king's input?
Could lords expand by buying more land from other lords, or perhaps conquering it from them?
As u/ttrombonist said, it is practically impossible to talk about medieval feudalism in this way, not only because the term medieval covers such a long period across a very diverse geographic range, but also because even for people who used words like 'vassal' and feodum/'fief', the words and the practices these words referred to were not the same and changed over time. Covering this topic in its entirity in one post is next impossible, but I will try to answer your question to the best of my abilities.
In the first place, the idea that under feudalism the entirity of landholding in a realm was in the hands of the king who then gave it 'in fief' to his main vassals, who then could do the same for their own vassals and so on and so on doesn't have much support anymore, independent of which position academics take in the debates referred to by u/ttrombonist. Kings just never had this kind of power, nor was there ever really a moment in the development of the post-Roman kingdoms were the king held all the land available to him. For example, when the Merovingians Franks created their kingdoms in what used to be Gaul, there was no such thing as feudalism yet and most landholders held theirs as full property, although concepts of usufruct did exist. Merovingian kings donated lands outright to their followers (called alienations).
Under the Carolingians this changed, mostly because the Empire did not really expand anymore after 800 and the pool of landed property became static, which created the need for rulers and high aristocrats alike to find new ways to reward their followers without decreasing their own powerbase. This gave rise to a boom in systems of usufruct, with followers gaining access to landed resources while the lands itself remained the property of a king, aristocrat or monastery. But again, this is not really feudal.
This also means that in none of the realms that developed out of the Carolingian Empire (mainly France and the Holy Roman Empire) kings did never have exclusive property rights. The same goes for areas like the Iberian kingdoms, England before and after the Norman Conquest, Southern Italy, Scandinavia or Central-Europe. Everywhere there existed traditions of private landholding outside of royal power, simply because these societies developed naturally.
The feudal system (in whatever form or to what degree it actually existed) developed out of these societies and there was never a real clean break, or at least that is my opinion. It is very much possible that the only real difference between a fief and an allod (the term used for full properties in the Carolingian Empire) was that a fief combined rights to land and jurisdiction over the people living on it. It could also just be that a fief was the term for a property held by a nobleman instead of a commoner, which is one of the things Susan Reynolds argues. And throughout the medieval period after the year 1000, when there are changes taking hold that go in the direction of something that could be called feudalism, 'allodial' property still was a thing. It is also important to keep in mind that holding a fief was primarily a social relation between a vassal and a lord. It implied a hierarchical relation between people and as such was probably much more important to express (relative) status and social obligations that actually organising property ownership.
This makes the question of whether lords were able to trade their 'fiefs' a difficult one, because they were not just property as we understand it in in the 21st century. It had a lot of social value and was not just the ownership of a piece of land, but could also include the right to certain taxes, judicial powers and political influence. So we need to ask the question, Why would you want to sell it? Getting rid of a fief because it is, let's say, not close to your current main seat of power is not something you would want to do, because having this fief and thus probably followers there actually gives you influence in a region that you can't visit in person much. Medieval aristocrats also usually were not in the mind of selling their stuff. They were very much oriented to extending their landholding and socio-political influence. 'Alienating' a fief would cause relations with your lord to deterriorate, which is not something you want because he is usually also going to be your patron and someone giving you career opportunities. But it did happen and in his book The Aristocracy in the County of Champagne, 1100-1300 (2007), Theodore Evergates dedicates an entire section to 'The Market in Fiefs' which existed there since around 1130-1150. A lot of times, this was done by nobles who wanted to acquire funds to leave on Crusade to the Holy Land or increase their cash funds, for example to provide for dowries.
I hope that this at least answered your question a bit. Unravelling every aspect of it would require too much side-steps to do in this answer form, but if there are unclarities or if you have other questions, feel free to ask.
If it's something you're interested in, I also started a blog about the Middle Ages in which the first topic I tackle is exactly feudalism: https://worldsthepast.wordpress.com/
The main literature I based myself on is
- Framing the Early Middle Ages: Europe and the Mediterranean, 400-800 (2007) by Chris Wickham
- The Carolingian World (2016) by Marios Costambeys, Matthew Innes and Simon MacLean
-Reframing the feudal revolution: Political and Social Transformation between Marne and Moselle, c.800–c.1100 (2013) by Charles West
- Fiefs and Vassals: The Medieval Evidence Reinterpreted (2001) by Susan Reynolds
- Feudalism: New Landscapes of Debate (2011) by Sverre Bagge, Michael H. Gelting and Thomas Lindkvist
- The Aristocracy in the County of Champagne, 1100-1300 (2007), Theodore Evergates
It's very difficult to talk about "medieval feudalism" as this uniform method of social and political organization across medieval Europe, which would refer to a 1000-year-long era across a landmass that stretches from the Atlantic coast to the Urals. While you wait for an answer to your question, please check out some previous answers about feudalism, and how it never really existed as a uniform concept in medieval Europe.
u/idjet's answer to Did Feudalism Actually Exist?
The Feudalism Didn't Exist AMA, with answers from u/idjet and u/TheGreenReaper7
A discussion of the Recent History of Feudalism, by u/Miles_Sine_Castrum, and
How does the current shift away from the concept of "feudalism" in medieval scholarship impact the understanding of statebuilding and the centralization of power in the early modern era?, with answers by u/Valkine and u/sunagainstgold