What are the implications of building a private airfield in the United States?
This has been somewhat covered in other questions here. You can find the legal requirements in the answer to this question (somewhat of a dupe to this question). There are some notes on security in this question.


  What would it cost to maintain this installation, above and beyond the
  cost of maintaining any piece of property of this size? What's
  included in these costs?


For a grass strip you will need a good ride on mower and possibly something to level/press the ground. Maybe some filler if there are any divots etc. But all in all the cost to maintain a strip of grass is pretty cheap. 


  Are you required to pay to have an airfield listed on charts?


Im not sure of this one but there may be some requirements you need to meet which could cost you money. 


  Do the parameters I've listed seem reasonable for the requirements
  I've mentioned?


Yes, 22-2500 is more than common, FWIW a bit on the short side but you should have no problem getting your common GA planes in and out of there. Keep in mind that with trees at the end and on either side this could get tight. In reality runways (at least nice paved ones) have a lot of clear space around the immediate area.