Remember that trade does not take place between countries, it takes place between individuals.
Sorry, that's not "completely" true. How is a trade imbalance settled? What happens when there's a $1B trade deficit?
That trade deficit, roughly equivalent to the current account deficit, is counter-balanced by a capital account surplus. If the people in Country C are not buying enough products from Country U, then they are accumulating dollars or dollar-denominated securities. When they have more of these securities than they want to hold, they try to trade them for something else like yen or rubles or yuan.
When the people in all countries have more than they want, when they are all looking to dump surplus dollars, then the value of those dollars declines.
(Note that a trade deficit alone does not trigger dollar weakness, only more dollars floating around than what people want to hold. Also remember that money has several purposes including a medium of exchange and a store of value. And the usual method of making a currency more valuable is to raise the interest rates, to encourage people to hold more of it and not dump dollars on the market.)
Sometimes governments try to impose currency regulations, to limit the ability of citizens to trade their depreciating currency for others which maintain their values. I think Great Britain did this after WWII until the 1960s -- which created a lucrative black market.
I think I said this before, but tariffs are taxes on consumers. Small tariffs result in tax revenue because they do not discourage purchases to any major extent. Big tariffs produce little revenue because no one pays them. I suppose a big tariff on steel or lumber or cement benefits domestic producers, because there are few or no substitutes. But a big tariff on fruit or chickens can result in a change in consumption patterns, leading to more demand for other items. BUT recognize who is buying these goods, or not buying them: individual consumers, not the countries where they reside.