"While performing a primary attack at attack range 0, attack dice cannot be added."

[Archistopheles]

Page 5 of the RR, under 2a "Rolling dice" it says the Title; emphasis on the word "added".

Does this apply to effects that "Add 1 (Focus/Blank) result", "Roll 1 additional attack die", or both?

[AMG_Plummer]

This applies to both adding dice to the attack roll,  and adding results, provided it is the attacker that is adding those results.

The statement that dice cannot be added means that additional dice cannot be rolled. Adding results is a modification of dice, and attacks at attack range 0 cannot be modified, except by the defender.