I agree with my colleagues that you should consult an international business attorney in your area, and use your list of questions as a starting point. One additional consideration is whether the products that you intend to import violate anyone's intellectual property in the United States. Depending on the product, a patent or trademark search may be necessary.
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These questions are really beyond the scope of what the lawyers here at Avvo can handle. You need to sit down with a good business lawyer in your area to discuss your options, because there are many questions that need to be answered. There are quite a few good lawyers on Avvo that are in the Southland.
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I specialize in incoming foreign trade with the US. Your questions are somewhat unclear (e.g. "two different business entity", or "legally allowed foreign company".) Some products require import licenses, some don't. Issuing shares is a complexity unto itself, and is also very fact specific depending on your situation and your goals. It is much too extensive for an Avvo answer.
The above is general legal and business analysis. It is not "legal advise" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.