startig business

hi,

we are an Egyptian family and one of our children is an American citizen.
Can we start and operate a business in usa ? And can we rent a store ?
thank you in advance.

Your US citizen relative can start whatever business he wants, enter into leases or whatever else that is requird.

You can not come here without securing an appropriate visa (which should not be too involved for many of the direct relatives).
You can not work here (even in son's business) without a visa that permits that (again, it's doable).