To answer your questions:
1. I don't know of any agents that'd pick up a non-profit book for a niche market like this. These are the kind of projects that you do parallel to a non-profit, so I'd look into Ugandan non-profits focused on literacy, education, etc.
2. Always, always expect to work with an artist if you're not one. Publishers will provide an artist.
3. Drawings by kids for kids... I'm not a fan. You want to create a professional, quality product, and while pictures drawn by Ugandan children would be sentimental, I don't think sentimentality always sells. Maybe you could include some, but not for the entire book.
I would partner with an Ugandan non-profit that focuses on education for children, then launch a kickstarter.com campaign where the book or segments of the book are "rewards" for donating. Use a segment of the funds to polish the picture book (working with printers, designers, etc.) and to create a website so the book has a location where people can purchase it.
Best of luck!
Todd, thanks so much for your helpful advice.