You covered a lot of things here, so I'm likely going to jump around a bit.

The expressed opposition to "multiculturalism" is, in my estimation, mostly rooted in simple fear.

It's a result of the egoist, most often not coincidentally of the Nietzschean variety, simultaneously lauding the will to power and fearing the expression of that by others, and particularly others of other cultures - cultures with norms they believe themselves ill-equipped to successfully overcome. They're attempting to proactively skew the playing field because they fear that if it really does come to a power struggle on a level playing field, they'll lose.

So you can't really investigate the argument with the hope of finding reason at its heart, because it doesn't spring from reason in the first place - it springs from fear. Whatever appearance of reason it might possess is simply there to put a gloss on it.

"Multiculturalism" is problematic in and of itself. It seems to mean something akin to simple acceptance of different cultures, but in practice, those who advocate it seem more often to desire the maintenance of discrete cultures instead of merely the acceptance of them. I can't help but think that a good part of that is simply because it's so often advocated by "progressives" who really have an interest in it so that they can leave their gated communities from time to time and go to quaint little shops and restaurants and street fairs. It's sort of a Disneyland/National Park conception of "multiculturalism" - what they really want is for those quaint little natives to remain quaint little natives so they can play tourist in their quaint little native neighborhoods. That's a viewpoint that, in my estimation, is rightly opposed. It should be noted though that, even with that, most of those who actually do argue against "multiculturalism" are in fact arguing against the first, more idealistic, and actually less common conception of it - simple respect for and acceptance of other cultures.

I think that the most notable thing about European culture is that, mostly for environmental reasons, it balances practical effort and leisurely pursuits in a way that put it "ahead" of most competing cultures. Most competing cultures either arose in places where the environment was more harsh, and thus the simple struggle for survival more time and energy consuming, or in places where the environment was less harsh, and thus there was less of a colorable need to organize and plan and to instill a work ethic that could then be bent to the desires of those empowered to organize and plan. Simply by being in the right middle ground between those two extremes, European culture could justifiably instill a work ethic, but have a population with enough time and energy left over from the mere process of surviving to bend them to other pursuits that tended to "advance" the culture.

What my question boils down to is, are the norms that support the market held up by culture?

I'd say only in a limited sense, which is to say, you might have a culture that's orgainzed in such a way as to inhibit or advance "the market," but that's about the extent of it. As an-caps themselves are generally wont to point out, "the market" is simply a natural expression of the fact that individuals possess different skills and different things and it's convenient for all parties if there's a way to exchange those skills and those things.

Or does culture begin to imbue these norms once the society is interconnected enough for them to emerge?

I think that's far more likely. And it should be noted, in that context, that "markets" the world over are not greatly different from each other. They might differ in detail, but the fundamental arrangement of them is notably similar. Aside from having to learn local currencies, values and specific tactics and traditions, anyone who's familiar with the workings of a market in any one place can almost certainly function in a market in an entirely different place.

I don't know if any of that answers anything, but there you have it...