For #1: the WB set in ACR. Initially, this is the "As Shot" WB which is usually the camera's suggestion, as you say (though it could be a fixed WB setting if you chose a manual WB using the in-camera settings). As an example, suppose you created a profile for 2 illuminants, approximately A (2856 K) and D65 (about 6500 K). If you drag the temperature slider in ACR towards 6500 K, you'll end up using more of the color matrix and color table for the D65 "half" of the profile, and if you drag the temperature slider in ACR towards 2856 K, you'll end up using the color matrix & table for the A "half" of the profile. And if you're somewhere in between, like 5000 K, you'll use a mix of both.
For #3: The wavelength. There are infinitely many lights that map to the same correlated color temperature (e.g., 5500 K). In practice, for example, you may have a flavor of natural daylight (some mix of sun & clouds) that gives you 5500 K CCT. You can also have fluorescent tubes that will get you about 5500 K, too. But the color rendering produced by the two lights can (and often will) be quite different, for certain materials. This poses a problem if you're trying to use a color profile made for one illuminant (e.g., the daylight one) for images shot under the other (e.g., the fluorescent one). In short, the CCT (or even a temp/tint pair) is not enough to describe the illumination. Having a spectrum of the overall ambient illumination (i.e., relative power at each wavelength) would help a lot, but this information is generally not easily available.