Assuming that you set up the LLC in Wyoming, you are correct, you would have no US based taxes. If you set up in another state you might have taxes depending on the State.
US LLC is︀ a pass through entity unless you elect otherwise, so no dividend tax in US.
US does not have VAT. No idea how this effects you in your home country or︁ EU.
It is︄ not a tax return it is an informational return that gives information on the foreign︅ owner of the LLC and monies sent to them. It does not trigger tax liability.︆ You will have to track income and expenses.