Is the person afflicted with obsessive doubts (waswas) held accountable for the blasphemous whisperings that accompany him when committing sins, or only for the sin itself? And is my understanding correct that disbelief (kufr) only occurs through intention and the heart's tranquility with it?

Seeking refuge (with Allah) and repelling whispers (waswas) is correct. The disobedient person is held accountable for their sins, not for the whispers accompanying them. Hating thoughts of disbelief is a sign of faith. Our reason for saying that the increase in whispers due to masturbation confirms the obligation to stay away from it is to close the door to whispers from the outset; for prevention is better than cure, and staying away from the cause that brings whispers is better than engaging in it, especially if the cause is forbidden. We did not intend accountability for whispers at that time. We advise you to remain steadfast in repelling whispers and seeking refuge with Allah from them, and to keep in mind the distinction between the sin of disobedience and accountability for whispers, along with the obligation to repent from all sins.