Tariffs can have some unexpected effects. PBS ran a story for example how increases in steel tariffs that were not coupled by increases in nail tariffs resulted in more nail imports and hardship for a local US nail manufacturer.
As another example, and more generally
Businesses like Detroit Bikes react to tariffs in many ways, and one of the most significant is in finding alternate sources of goods. If Pashak succeeds in finding cheaper substitute parts, he keeps costs down on his bikes, which range from about $400 to $1,250. That then blunts the overall price increase for his customers.
Economists call this "substitution," and say it affects how much consumers pay for tariffs.
"The impacts of these wars depend heavily on the substitution effect," says Amit Khandelwal, a professor of international business at Columbia University.
But finding replacements for things like bike chains or software chips is considerably harder; factories can't just be ginned up on demand. "Generally, the more specialized products often take longer to substitute," Khandelwal says.
Other indirect effects include hardship in other sectors due to external retaliatory tariffs. The US agriculture being the prime example here, with some bailouts put in place to compensate.
Ultimately the trade war is blamed at least in part for the current global manufacturing recession/slump. The US took longer to feel that, but apparently it's hit home as well. (See also my question on econ.SE on that.)
As far as your more focused questions, US steel imports did fall some 12% in the first this year. Actually 14% including August. US steel prices have generally followed the vagaries of tariff announcements:
US steel production did go up to 2014 levels (previous source) after tariffs were enacted.
Production is up since 2016, but it has been higher as recently as 2014. Figures from the U.S. Geological Survey, which gets its data from the American Iron and Steel Institute, show an increase in raw steel production from 2016 to 2018 of 10.8%. Production hit 87 million metric tons in 2018, but was 88.2 million metric tons in 2014.
“These are improvements, but we’ve seen improvement of similar double-digit magnitude in the past,” John Anton, director of steel analytics at IHS Markit, told us in citing monthly year-over-year production increases, from a high of 9.1% in January to a low of 3.1% in June. “We’ve also seen deep cuts” in production in the past, he added. “But production is up.” [...]
The price spike in 2018 was unsustainable. U.S. steel prices “went up by more than the tariff rate,” said Anton, who put the increase at about 53% higher than European prices. “When you go too high,” he said, “you’re going to attract imports.” Prices now in the U.S. are only about 7% higher than European prices, he said.
Even the fairly conservative, but free-trade leaning American Enterprise Institute ran this story:
$900,000 per job
That’s the cost to US consumers of Tariff Man’s steel tariffs as calculated by the Peterson Institute for International Economics and reported by the Washington Post “Trump’s steel tariffs cost U.S. consumers $900,000 for every job created, experts say“:
[...] The cost is more than 13 times the typical salary of a steelworker, according to Labor Department data, and it is similar to other economists’ estimates that Trump’s tariffs on washing machines are costing consumers $815,000 per job created.
Trump has [falsely] claimed that other countries are paying the tariff bill, but evidence shows the tariffs are taxes paid by Americans. U.S. companies that buy metals are either absorbing higher costs or passing them along to consumers. General Motors and Ford said Trump’s tariffs have cost them $1 billion each.
[AEI author ponders]: More “winning”? Or more “backfire economics” and costly “economic suicide bombings”?