Is any of this dependent on the size of the ship? Yes, but there are various factors and trade offs. A factor of your total resistance is your viscous resistance which scales geometrically with your wetted surface area. You can make your ship shape a rounded box, which maximizes cargo for surface area, but then causes more hydrodynamic drag. Or you can make the hull shape a tapering hydrofoil to solve that, but increasing the surface area underwater if you try carrying the same cargo. The choice to go with ends up depending on what the ship is carrying. For instance, oil tankers will go with the rounded box because their cargo is practically the same density as the water so they have to carry it low. Container ships can afford to stack their cargo very high and can even play games with arranging it by weight, so the can get away with a slight, or slender hull below water without sacrificing much cargo. In trade they can get more speed. Bulk cargo ships will fall somewhere in between. The draft and beam required for ports visited and canals traversed all factor heavily into the choice as well.

Is this a bigger problem with big sails? I can imagine with a really big airfoil sail it might be hard to get the ideal angle / shape. But, if it’s a square-rigged ship it seems like it would be less sensitive to turbulence because it’s not an airfoil?

They actually still work as airfoils, ideally. The best way to extract the most energy from the wind is the angled sail working as an airfoil. This, of course limits how far apart the sails can be. I imagine it also places some limits on overall size based on the balance of more sails vs bigger sails. The height will be limited by the righting moment of the ship, so you can't just make them crazy tall without also needing to make the ship so wide it can't fit into port, though I guess you could play games with outriggers to push that boundary.

And a modern cargo ship goes about 20 knots, right? But, does that mean that you could get maybe 16 knots out of the engine and 4 from the wind? Or is it that the wind can supply 1 MW of power, which is enough to move at 4 knots, but if you want to move at 20 knots you need 30 MW of power, so the wind would only supply about 3% of what you need, so it might not be worth it for all the added complexity?

24-34kts is what I worked with. I'm not sure exactly how the energy would be combined, but this is essentially what they're doing with these sail kite ships. It only saves a few percent of fuel, but that is nothing to sneeze at. I've seen various articles about the project with the kite since 2007 all claiming various savings, but it's supposed to pay for itself in a year or two, I've heard. It certainly feels worth adding, to me, but I don't manage a shipping line.

And, because petroleum-based fuel is very cheap because you don’t have to pay for the impact it causes, you can get an incredibly powerful engine that doesn’t cost an absurd amount to run. So, the additional cost to ship things at 30 knots using vast amounts of very dirty diesel is low enough that it’s still worth it?

Heavy fuel oil makes diesel seem squeaky clean by comparison, but it makes up for it by being even cheaper and containing more energy. The energy is so great, that all the fuel and engine space take up a relatively small amount of volume compared to the cargo. And you can cram that fuel into all the strangely shaped parts of the hull that would otherwise just contain ballast water. They actually do put work into cleaning up the exhaust, at least in reputable shipping firms. There are exhaust scrubbers that pull NOx, SOx, and particulates out at the same time as they recover waste heat. The output is still pretty foul, but the scrubbers take a big chunk out without much negative impact.

If you wanted to go post-apocalypse mode though, is there any size-scaling thing related to ships that means that big ships are impossible to scale as sailing ships?

Just the speed and overall size. Like, worst case you could always build a wind energy storage system to capture power from wind turbines, save it in power cells of some kind, then release it in bursts.

I don't see why you couldn't get traditional speeds doing square rigs on a repurposed container ship, but maneuvering would be hard. I don't know much about tall ship design, but I think they have to be able to turn very well to really tack with the wind.

If you wanna go real apocalypse mode to though, just cobble together a crude nuclear reactor in the boilers of a steam ship and steal some fuel. You'll probably die from cholera before the radiation gets you, anyway!

I still really want us to go in for nuclear cargo ships though. The NS Savannah is so cool. I've gotten to tour her a couple times in Baltimore. They want to turn her into a public museum ship with a reactor mock-up you can walk into, but need a few million in funding to properly decommission the real one.