About Feudalism (Section Edited)
In Feudalism, we start at the top with the ruler, who is essentially a landowner. He or she then doles out parcels of land to lesser lords and/or ladies, who are then responsible for the occupants thereof. Depending on the size, you could have many layers, from King, to Lord, to Dukes, to Barons, Counts, Viscounts, even Marquises, and so on and so forth.
Initially, the Feudal Lord ensured that farmers would be able to farm in peace by keeping a standing force and sending them out to kill bandits, rival forces looking to claim territory, and even packs of wolves or bears that threatened crops and livestock. The knights who became lords were the only ones capable of fighting off these threats, and so therefore became landowners with "tenant farmers".
In exchange, the farmers handed over their crops or livestock, as a "rent" or "tithe" or something of that nature. They paid for the privilege of using the land with goods.
The only laws were those made by the landowners, and only the laws that could be enforced physically were those that were considered true laws. Over time, the knight became "king" and was able to then dole out land to his trusted family and friends. However, the whole plot of land (the "fiefdom" or "kingdom") was still his and he held dominion over it.
Since this is your world, you don't have to follow the strict timelines of the feudal system in our world, but I would like to point out that by the time cannons rolled around we had largely abandoned the feudal system in favor of the monarchy, which is entirely different.
EDIT: See the comments below for a more realistic description of feudalism. In the early stages, there was no cash-based economy, therefore Kings were forced to "pay" their knights in land, which the knights then lived off of. This causes a problem as the more land the king gives away, the poorer he becomes, and he has no way of collecting anything from the land he gave away. The knights can then use their land and power to usurp the king, causing instability and general problems which went on throughout the feudal period.
As you had initially requested something "genuine" rather than "factually accurate", I outlined a cash-based feudal system below, which isn't entirely historically accurate. Further research into the issues of the feudal system might benefit you if you want it to be more historically accurate, but hopefully some aspects of my answer will still apply.
Responsibilities
Your lady's primary duty is to make sure that her people, whether they be villagers on the edge of her territory or villages closer to the center, are safe. 878
In addition to physical threats like those listed in the last section, this may also entail watching for plague-bearers, monitoring trade caravans that come through her land, keeping an eye on the weather, and watching for stages of drought or blight.
Vassals are given land to monitor because their Liege or King is too busy/rich/occupied to watch over every parcel of land. I liken it to management in the corporate environment. Your King and his advisors are the Chairman and his Board of Directors. They demand that profits continue to rise, and that their positive reputation is maintained. In order to do that, each "department" or parcel of land must produce money, through taxes, tithes, or something similar. This job falls upon upper management, who must ensure each staff member (the peasants) is performing efficiently, paying rent, and farming as much as possible so they can be taxed. Her responsibility to her king or liege, therefore, is to pay him the profits of the land, whether that be in taxes or tithe, or "donations", and to report to him that everything is going well.
Your lady can actually have as much or as little control as she pleases, but her goal is to maintain the population. Peasants have no ties to the land that they farm, so if a plague, blight, or poverty prevent them from working or surviving, they will begin to die off or will emigrate elsewhere. If she exerts too much control, demands too much in tithe, or on the other end of the spectrum, if she refuses to guard against attacks, or refuses to maintain certain things, she will find that her lands will be deserted, she will have no one to tax, and therefore no income.
Ideally, she wants to establish a safe and stable economy. Responding to immediate physical threats quickly will show the peasantry that she cares for their welfare. Day to day she should open herself or her stewards to inquiries from the people. Do they need to dig an additional well in order to get more irrigation to crops? Do they need paved roads in order to transport their produce to the village to sell? 222