Except, of course, for some boards such as the ESP8266 where pins are referred to with a D prefix unless you want to refer to the actual pin on the chip, in which case you leave off the D prefix. To complicate things further there is not a 1:1 relationship between the D pin numbers and the chip pin numbers
It is, however, generally safe to use the pin number as printed on the board
If you think that you can write a better explanation of pinMode() than pinMode() - Arduino Reference then please feel free to post it here
The analog input pins can be used as digital pins, referred to as A0, A1, etc.
seems quite clear to me and there is also a link to https://www.arduino.cc/en/Tutorial/Foundations/DigitalPins which contains onward links to details of other functions
Don't jump to the conclusion that everybody actually reads the reference pages and if they do that they take any notice of them and don't forget that IDE contains examples of many of the Arduino functions