The goal when you first establish contact is to ask questions that will help you ascertain whether that organization is the right "fit" for you and your project, in terms of its mission and focus.
Gauge whether they would have any interest in you and your project. Will they see you as a potential collaborator whose presence with them for 9-10 months will be an asset to them? Or do you get the sense you will be a nuisance to them? (Obviously, how they perceive you may depend in large part on how you approach them.)
If things are going well, consider asking them for their input on your project. See whether they think it is viable, feasible, and important for your field or that country. Ask if they have suggestions for directions your project could go.
Eventually, you will need to know how, specifically, the organization will be able to support you in your project goals. What resources will they be willing to provide you while you’re there? (This may include advising, use of material resources, access to their professional network, etc.)