Suggest you conduct a google search for literature using your key questions as key words. Many writings on the role of agriculture in economic development will have elements of these issues.
For income generation it will be better to apply agricultural household model which can help to work on labor force, factors of production and supply. this model is targeting on the maximizing the utilities of the farm owners subject to different constraints on the farm activities.
On the other direction you can apply production function with different parameters to assess their contribution to the farm income of the households.
I just find these literature that can help yet it will be nice to read more on production economics literature