Can a foreigner (non-US citizen) register a sole proprietor business in CA?

Hi,

I have a question, can a foreigner (non-US citizen) register a sole proprietor business in CA?
While this is registered, can the foreigner operate the business outside of US?
And as a piggy-back question: just in case I need to be physically hands on with the business, is there anyway I (as a non-US citizen) can be in US to operate the day to day function?
I really appreciate your input and feedback.

Thanks!