Great question!

One of the reasons why libertarians have had a suspicious admiration for the Middle Ages is that feudalism turned what we think of today as the state/public sector (which is different from the public sphere b/c Habermas) into personal property rights.

In a feudal contract, the king gives taxation power, judicial authority, etc. over a geographically-defined area to an individual leasee, in return for that leasee providing a certain amount of military service. (Which in turn means that these leasees are also exercising significant amounts of military power, so there goes the monopoly on force.) And as I’ve discussed before, this grant changes over time from what we might call an outsourcing contract that can be reassigned to an inheritable estate, which makes it ever more propertyish than before. And when, over time, people are allowed to sub-lease parts of their grant to other people, it becomes more propertyish still.

This blurring of the public (taxation, military power, judicial authority) and the public goes all the way up the chain. For a long time, there wasn’t a clear distinction made between the king’s personal household and the state: we can see this from the fact that a lot of the offices of the privy council use the same names as offices on private estates, or from the fact that there wasn’t for a long time a clear separation between the personal income of the monarch and the revenue of the state (see for example the long bureaucratic struggle over whether the Office of the Wardrobe (which was supposed to pay for the king’s household but ended up paying for wars) or the Exchequer would be dominant in finance).  

This begins to change in the Early Modern period, where you see the emergence of professional bureaucracies who can more efficiently collect taxes, keep accounts of moneys received and spent, so that ever-growing armies can be outfitted, supplied, and paid promptly enough to keep them from deserting. (This is all very much a work in progress.) 

Not coincidentally, the growth of these large royal armies coincides with a period of struggle between monarchs and the nobility over the boundaries of the public and the private: whether the king’s courts could overrule local manorial courts, whether nobles could fight private wars, fortify manors without royal permission, keep more men under arms than their feudal service allowed, and whether royal tax collectors could directly extract revenue from their fiefdoms without the lords’ being able to intervene. 

To answer your second question, there was a distinction between various income streams: in addition to feudal rents, the use of monoplies on mills and the like were called banalities (great name, imo), chevage or chiefage was a poll-tax paid by villeins, income generated for lords from fines in local courts was called the third penny, the sales tax on livestock was called the toll tax, and then there were a large number of what were called feudal incidences (fees paid when a peasant got married, inherited land, or died, etc.). And to go back to the paragraph above, one of the reasons why so much conflict arose over judicial reforms was because the king was often muscling into revenue streams that the lords considered their personal property right as opposed to public finance.