Celsius and Fahrenheit doesn't work as an analogy because the rate does not change over time as it does with currencies.
There may be some offset for goods imported from the US, but that's a minority of consumer goods globally, and even then, the purchase currency will usually still be the local fiat, and then the attractiveness of the US index fund still has to be weighed against the performance of non-US-based indices in that same local currency as opportunity cost.
I don't understand this question, are you asking if material goods and services in Europe, which uses EUR, "somewhat" follows the S&P, a US stock market index?
Do people do this? Up until some months ago, I was heavily invested in some US companies, and I never actually held USD in my accounts at any point. I used EUR to buy those stocks, the conversion happening together with the purchase, and same thing when I sold them, I received EUR ultimately.
I know I could have another account in my bank with USD set to the currency, I just don't know why'd anyone would want to, when you can convert at the point of sale/purchase. Of course, if you're doing forex trading or whatever, that might make sense, but I don't think generally people hold USD to buy/sell US stocks, because you don't have to.
Approximately no individual does this. Some companies may hold some foreign currency reserves, but even there it is not _particularly_ common in most cases.
As a European, I have never, in 40 years, had any USD, except a small amount of paper currency. If I'm buying something made in the US, I'm probably buying from a local vendor, or else will convert on the fly. If I'm visiting the US, I'll convert on the fly (this is even cheap, now, thanks to neo-banks). I own a bunch of US equity, but indirectly via a euro-denominated global market index fund. This is fairly standard. In general it's only common for individuals to hold foreign currency where the local currency is particularly unstable.
... Wait, why would you expect the price of goods to follow the valuation of, well, any market index, never mind one specific foreign market index? Like, I don't understand why you think that would happen. If anything, you'd expect a minor inverse relationship, at least on a global scale; rapid growth of cost of goods indicates inflation, which implies central bank tightening, which tends to depress stock values a bit.