>How does that help? Isn’t the country that has lax environmental laws and can sell cheaply going to win over the country that has tough environmental laws? (Genuinely asking, my degree is in engineering not economics.)

You're correct it doesn't help. Either you raise the price of the foreign good through a tariff or other sneaky measure or consumers will buy it and amplify the externality.

>And do these models account for changes in dynamic equillibrium? E.g. a foreign country engaging in dumping ends up killing the domestic industry? It seems odd that exercise of monopoly power can lead to deadweight losses in a closed domestic market, but a country engaging in anti-competitive measures overseas is best handled by doing nothing.

They don't and even Krugman would admit to this now. It's actually funny that we're using Krugman from 1998 because if we take his trade talk from just four years earlier it's clear he thinks distribution could be a problem:

The truth, however, is that fears about the economic impact of Third World competition are almost entirely unjustified. Economic growth in low-wage nations is in principle as likely to raise as to lower per capita income in high-wage countries; the actual effects have been negligible. In theory, there are some reasons for concern about the possible impact of Third World competition on the distribution (as opposed to the level) of income in the West, but there are few signs that such concern is justified in practice, at least so far.

https://hbr.org/1994/07/does-third-world-growth-hurt-first-w...

And then if we zip past 1998 back to the present day he's once again walking back on the pro trade rhetoric here:

But it’s also true that much of the elite defense of globalization is basically dishonest: false claims of inevitability, scare tactics (protectionism causes depressions!), vastly exaggerated claims for the benefits of trade liberalization and the costs of protection, hand-waving away the large distributional effects that are what standard models actually predict.

https://krugman.blogs.nytimes.com/2016/03/09/a-protectionist...

and here:

That said, not all free-trade advocates are paragons of intellectual honesty. In fact, the elite case for ever-freer trade, the one that the public hears, is largely a scam. That’s true even if you exclude the most egregious nonsense, like Mitt Romney’s claim that protectionism causes recessions. What you hear, all too often, are claims that trade is an engine of job creation, that trade agreements will have big payoffs in terms of economic growth and that they are good for everyone.

Yet what the models of international trade used by real experts say is that, in general, agreements that lead to more trade neither create nor destroy jobs; that they usually make countries more efficient and richer, but that the numbers aren’t huge; and that they can easily produce losers as well as winners. In principle the overall gains mean that the winners could compensate the losers, so that everyone gains. In practice, especially given the scorched-earth obstructionism of the G.O.P., that’s not going to happen.

https://www.nytimes.com/2016/03/11/opinion/trade-and-tribula...

The answer to your questions are all basically no and I would blame it on the blurring between economics and folk economics. I also hold an econ degree and I see this almost everywhere - someone holds up a simplified model, claims it proves free trade is good or minimum wages are bad or whatever political issue is hot and then they close the book. There's tons and tons of relevant literature on all these theories and once you dig into it and the models become more sophisticated then many of the standard things we expect the model to say morph and change. But this academic economics is usually crowded out in public debate by the simple models and easy free market talking points.