How to correct colors in RAW data?

I want to correct the color of RAW data by myself. To do this, there are two important steps:

1) white balance

2) Color correction

There is a very good tutorial on how to estimate this color correction matrix. However, there are points that confuse me in the color correction pipeline (the questions can be so simple, I am very new in this field):

1. There are 9 coefficients to obtain a direct matrix, which transforms the color space of the camera into a color space independent of the device. How can 3 coefficients be sufficient to determine the white balance?

2 X-Rite gives the reference values ​​for each patch in the color checker. The reference values ​​are obtained in the CIE D50 environment. My question is whether the level of illumination is important in this environment? I mean that the reference values ​​can be obtained in a very dark environment and that we can capture our very bright photo and the same color temperature environment.

3 If we have our own chroma meter, in what environment should we do our tests? (EV, color temperature)

4 In this document, it is indicated that each line of the color correction matrix must be transformed so that the white dot in the sensor space is identical to that of the device independent color spaces, such as XYZ or Lab. For this purpose, each line is normalized with its sum. This operation actually changes the matrix significantly. Should the color correction matrix not handle the white point when solving the opposite problem?

5 Is the color correction matrix estimated for all environments? Do ICC profiles include every possible case within?