Farmland usage greatly depends on the type of food being produced. Growing grains might require less farmland to produce enough to feed one person (for one day or for one year) than needing farmland to raise livestock or grow fruits and vegetables. Because of the different amounts of farmland needed to produce certain crops or livestock, you might look at either simplifying the problem -- either looking at a person's diet, and equating that to only one food source that is fairly universal (like rice) or looking at another unit of measurement that can be studied across different food sources, like water -- it takes water to grow crops for food, and it takes water to grow feed for food animals. The amount of farmland needed to feed a person greatly depends on diet -- meat production uses a lot more land than vegetation productions.
Check out the first link, and it helps to answer some of your questions with some actual numbers.
The second link mentions that "At least 1.2 acres per person is required in order to maintain current American dietary standards."
The third link states "Agriculture is the world's biggest user of water -- it takes at least 2,000 liters to produce enough food for one person for one day. That translates into 730,000 liters annually per person."