I did it for MMS by asking for it on the Webmaster Support forum. If you know other moderators, that might help to push it. It took me a few months; as I'm not a moderator. The Webmaster is the one who would create it, I think. Maybe the moderator of that forum did it. No one answered my recommendation. It just showed up one day. I think anyone can post questions. That could be a problem. You might also ask for exclusive control. It will be empty and show up as a link at the top of the forum.
Not a lot more work. You link into FAQ, ask a question (doesn't really have to be a question), then post an answer.
You have some really good stuff here. You probably really do have some Frequently Asked Questions already. With a FAQ, you should not have to answer the same question over and over.
*edit* A really extensive FAQ can be seen at the Iodine Supplementation forum. Wombat went through a lot of effort to set that up. You should check it out for examples.