Hope,
it is really not that confusing and the previous posts have raised all the elements.
The County zoning laws are explicit about the land uses in ag land. To understand this, read the zoning code.
A subdivision may adopt CC&R's that impose rules that are not imposed by the zoning. To understand this, read your CC&R's.
As an example of what CC&R's can do, take a look at Kohala by the Sea, a west side community of one acre ag zoned lots. Not only no roosters or livestock, but you must build a minimum of square footage, you cannot put up an antenna, you must have your paint and roof colors approved, you cannot build over a certain height, and so on and so forth. It is very controlled so that it will all be high end. As a result, most properties look a lot like this:
http://www.bigislandreale.com/North%20Ko...27126.aspx
and lots that initially sold at 99K now sell for 375K even in these times.
When you ask how it was meant to be ag if no crops were contemplated - well, first you really should read "Land and Power in Hawai'i" - Google Books has the whole chapter on Puna Subdivisions online and I linked it recently.
Also, if land is not conservation, and is not commercial, and is not specifically created as residential, on this island the default is ag. It's not like the default is residential and land must be shown to have agricultural promise to get that zoning. Residential zoning is harder to get and harder to develop, as I understand it. When I lived in Hilo, an adjacent lot that was residential was an ornamental ginger farm. Our house, built in 1950, had been an anthurium growing operation. So you can grow crops on residential zoning and on small lots.