You might want to consult a professional lawyers on these matters coz asking here in the forum you might get answers which are not true.
In particular, you can't expect any meaningful answer if you don't explicitly state your home country and the business you want to start (because that's the main factors determining whether legal restrictions apply, and to which extent they apply when your business is registered abroad).
Since it would probably unwise to discuss these things in an open forum, taking this to a knowledgeable lawyer is the right thing to do.
Note however that businesses that would be illegal in your country most likely don't become legal just because you're registering them in another country while still being the proprietor and hosting in your country. Of course, you may be able to hide behind layers of "privacy protection" and mail forwarding services etc. but these are most often signs that your business is shady at least and probably illegal too.
Onkel Paul
I should add that legality and morality are two different things. In some jurisdictions businesses that I consider morally wrong are legal, while in other jurisdictions businesses that I would be ok with are illegal. Doing illegal things that are compatible with your morals might feel ok but still could get you into trouble. In a democracy, there are processes to change laws (admittedly these work mostly on glacial timescales and are largely driven by those who are already in power). In an undemocratic country, you options are even more limited.
