Register company on H-1B, registration process for California and online business requirement?

Three questions:

1. Can I register a company/ business in the US on H-1B visa?
2. Does an online business need to be registered with the state or country?
3. If answers to the above are yes, then what's the registration process to register a company in California?

Let me start in order:

1. I cannot find any restrictions on visas to open a business in California. You can actually get a visa if you are planning to invest in a business in the United States so I don't see that H-1B is an issue.
2. A business is incorporated in a state and then you can do DBAs in other states.
3. You can follow one of these websites to do it: http://www.legalzoom.com/, http://www.incorporate.com, or find a lawyer that can do this for you.

I believe that you cannot create a company with an H1B visa. That would be in violation of the agreement: you are only allowed to work for one employee for each H1b visa and you cannot just create a company and give yourself an H1B visa; that's against the rules.

There are plenty of websites where people have asked this question.

Also, do not try to create company in your home country and work for that as well because if the US government finds out they could consider that as working for another employer and it could cause you problems.