Take the holiness of the Land of Israel, for example. In the famous Mishnah, the commandments connected to the land are mentioned as depending on its holiness. Does the holiness obligate the commandments, in which case the land is holy even today, even without observing all the land-dependent commandments, or do the commandments create the holiness, in which case the land is not holy since those commandments are not being observed there?

The question is not observance of the commandments but the obligation to keep them. If there is an obligation regarding the commandments, then the land is holy regardless of whether they are actually being observed. And that is so even according to Leibowitz, who always used to quote: "And what is its holiness? That first-fruits are brought from it, and the two loaves."

There are sources in the Sages and later on for both sides. Professor Leibowitz of blessed memory argued that this was Korach's claim, "for the entire congregation, all of them, are holy"—meaning that there is holiness in itself—but Moses held that their holiness exists only through the commandments. But in my opinion there is no need to connect the issues; rather, simply, Korach claimed that everyone had the same holiness, while Moses maintained that there are levels of holiness. In any case, the best-known saying of the Sages that there is essential holiness is, "A Jew, even though he has sinned, is still a Jew," and the opposing saying of the Sages is, "Our nation is a nation only through the Torah." Perhaps one could distinguish between individuals and the collective, but this requires further examination.

You're mixing apples and oranges, as is to be expected from such vague questions. "A Jew, even though he has sinned, is still a Jew"—that's obvious. What does that have to do with concepts of holiness? It's a simple halakhic claim. Even if he sinned, his mother is still Jewish.