Who writes the solicitations?
The answer to you question is that it varies both within agencies and across agencies. 

I have seen program coordinators write solicitations by themselves. I have seen them ask for scientists working within the agency to help write them. I have seen them ask for external feedback on research priorities. I have also seen scientists working within agencies write their "statements of work" for small, project driven proposals.

To answer your question for a specific agency and program, I would ask their coordinator or someone within their agency. You might also be able to ask a faculty member who has served as a reviewer for an agency.