Sodium chlorite will become activated as its PH is lowered. HCl does lower the PH, as does water. Yes, the HCl in the stomach will activate the sodium chlorite.
Your second question is a joke... Right? [sarcastic icon] In the broadest sense, salt may be thought of as a mineral, and sodium chlorite may be thought of as a salt. Sorry, this is the best I can do with this. [smile icon]
Sodium chlorite, when its PH is reduced, produces chlorine dioxide and chlorous acid. When chlorine dioxide breaks down in solution it forms chlorite and chlorate. There is also a small amount of chloride formed. Chlorine dioxide is unstable and I don't believe it can be measured in the body. Since it quickly breaks down, you should look at the chlorite ion. This seems to be the active chemical inside the body.
I am not aware of any hypochlorite that is formed during the breakdown of chlorine dioxide or chlorous acid in solutions. If any is formed, it is only in trace amounts and is insignificant. In air and in the presence of UV light the breakdown reaction changes and it is possible to form hypochlorite.
As far as the list of diseases cured, there seems to be some difficulty with documentation. There is some, but most of the reports are anecdotal. Without hard data I find it difficult to contemplate a common link...