Can a non-U.S. company own a U.S. company?

Yes, it can, provided the U.S. company is not S Corporation (or LLC taxed as S Corporation).

Is it better to own the U.S. company with my non-U.S. company from tax point of view?

Not necessarily. Ownership does not control if tax is due on US operations of the business. You will need to consider US taxation of non-resident aliens, and if the profits earned in the US are what is known as income effectively connected to operation of a US business, to understand how taxation would work in your specific case.

I own a company in my country, and I want to register an LLC to be owned by this company. Can I then distribute U.S. profits of this LLC to my company, and pay the taxes in my country?

It is not uncommon for an online business to avoid US taxation, but there are a number of specific factors that are unique to every business which you will have to consider. As you can see from a previous answer, ownership is not the only factor in defining if tax is due, so cases like this should be discussed with a US based tax professional

What if I own the U.S. company with my non-U.S. company, and the non-U.S. company will sell the U.S. company products for resale for the same price the U.S. company will sell them in the U.S.? I want to avoid having to pay taxes in the U.S.

You would not be able to sell at zero profit, due to what are known as transfer pricing rules, which establish how related entities located in two different taxing jurisdiction must establish the price they charge each other for items that are transferred between themselves.

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