Corn will use about 120-200 lbs f N, and 30-50 lbs of P and 30-50 lbs of K. (Actually it uses almost double that, but uses that amount to create the grain, the rest is returned to the soil....)
Depends how big a yield you are trying for, and what your soil has in it now, as how much you need to add.
Urea is a granular, spread it on the ground and work it in the soil so it doesn't eascape.
A 560 is a fine tractor for 20 acres; your trouble will be in renting fertilizer equipment, lot of places only have stuff for 150hp tractors any more, so you gotta see what works in your area.
Anhydrous is a rather dangerous gas that you need to inject into the soil with shanks. It is not dangerous at all after you get it injected, just as it comes out of the tank it is _very_ interested in absorbing all the water it can find, and if it comes in contact with your skin, eyes, or lungs it will damage or kill you. I think you would need a bigger tractor and a cab to use anhydrous yourself? Be sure you understand how dangerous it is for the 5 minutes it comes out of the tank as it seeks water - I got a drop on my thumb years ago, it took 4-5 years before the skin on my thumb was back to normal. A neighbor got a wiff in his eye, it messed up his vision a bit since. Treat the stuff with respect.
It costs a tad more - not much tho, and you could rent a spinner to put down a mix of all 3 - N, P, & K with the spinner spreader. It woulde be safer & your tractor would handle it.
Horse manure is good fertilizer. We don't know how much you have... What was the previous crop, soybeans, corn, or what? Makes a difference on the amount of N you need....