On your other questions, I think you are missing the bigger picture. The part you are missing is that EU exporters get a tax refund. The rebate the US is missing is an equivalent tax relief system. VAT-based economies remove tax burdens for exporters and keep them for importers.
To be clear, the EU is not “cheating”. Trump just sees the entire system resulting in a trade imbalance and the only mechanism he has right now is tariffs without overhauling the entire US tax code or some other similar relief system. There are other options that could be implemented like this and the one chosen was the tariff.