Hi Moyra,
These are good questions. It would be nice if someone could do some thorough research and get the answers. I will tell you what I believe at this point based on the limited investigation I have conducted. I could be wrong, but this is what I think right now.
I believe all 3 items do occur in nature, but all 3 are commodity items used extensively in various industries so the the most likely source will be whatever is cheapest to produce.
I believe sodium chlorite can rarely be found in deposits but usually it is produced industrially, and I don't think it comes from petrochemicals.
Calcium hypochlorite I believe is typically a mined product coming from certain deposits.
Citric acid comes naturally from citrus fruit and if you search around you can find it but only if it specifically says it is from citrus fruit. The cheapest way to produce it appears to be microbial fermentation of corn sugar and other ingredients. The company that says they are the leading producer in the world (Jungbunzlauer) uses microbial fermentation and I think I saw corn sugar mentioned in their literature. My guess is that the microbes are GMO and the corn sugar is from GMO corn, so tracking down a natural source of citric acid may be a good idea. If they do not tell you the source, then I would assume it is microbial fermentation.
Michael