I don't know their relationship, but in Salman Khan's TED Talk[1], Gates performs some closing remarks with him.
In the talk, he mentions that they're doing a pilot program with the Los Altos school district[2] as well, which I'm sure wasn't for free since it involved custom development.
Actually, it was totally free in terms of the school not having to lay out any cash. The reason we chose to work with them, however, is that they committed a ton of time from teachers, students, administrators, and parents to help us make the Khan Academy work better for the classroom use case.
The experience working with them has been fantastic. The teachers are fearless in the face of the significant uncertainty that introducing something like the KA in a classroom can create. They've been creative about experimenting with different ways of integrating KA into the classroom (trying things we didn't anticipate). Speaking as a UX designer, having nearly unlimited access to teachers and students for interviews and observations has been invaluable. Plus the teachers aren't shy about letting us know if something isn't working out. If anything, it feels like we should be paying them.
Sorry for not addressing that first time-round. We are funded by the Google and Gates Foundation grants plus private donations. As far as "most", I am not totally sure. I have very gladly stopped worrying about the particulars there as we've got some great folks (Sal, Shantanu, and Jessica) focused on making sure we're funded well enough to keep making progress at the rate we want. That frees up me and the rest of the developers to focus on building the product. Charmed life, eh?
He's indicated before somewhere that he is good with $1mm/year for operating costs (I think he said something along the lines of "If KA has $1mm/yr in revenue we’re good!", think it was in the Globe and Mail).
His lectures are hosted on YouTube (free) and he could crowd-source dev, design and QA. Also I think he is always going to be the only teacher - he seems to believe (not passing judgment here, just making an observation from what I 'sensed') that he's got a captivating charisma that people respond to, hence he’s best suited for conducting the lectures. I have enjoyed every lecture of his and think he has a point; he really is a good teacher.
Also, from his TED talk I got that his vision is a universal classroom - very noble. He might need translation, but again, that can be crowd-sourced too.