How about if the income is in your country of origin? Can't your side project just pay out where ever you're from? It's the Internet, websites aren't really located anywhere.
No :) It's not legal in America for people resident in America on an H1B visa to operate businesses.
You could just ignore this, like I do, but if you're in America on an H1B visa, which I'm not, then you're probably best off following the rules, lest they expel you and never let you back in, without giving you time to organise getting all your stuff back first.
To be clear, we're talking about running a country in your home country, not in America, while you are currently on an H1B in America. I'm sure you know more about this than I do -- could you provide me with a link? I'd love to learn more.
It's perfectly fine to own a foreign business (i.e., not located in the US). But it's generally a violation of the H1B to run (i.e., operate/manage/supervise) that business from the US because the foreign business is then generally treated as having a US presence. See "permanent establishment" and the US tax treaty with whatever country you're from.
