can an immigrant and citizen start a restaurant business together and the immigrant receive permission to be in the u.s like a workers visa or a permit or something because of having to own a business?
It sounds like you are asking whether getting a business partner for a green card or visa is like getting married for the same purpose. That is not a question for an internet website. Anyone who is seeking a visa should see an immigration lawyer in the area to determine the best way to proceed.
Yes, but having the business is not a guarantee that the immigrant will be granted a visa.