What is the ruling on Qur’anic verses coming to mind in the heart of one committing a sin, even though he does not stop the sin or distract his thoughts from it? And is that considered disbelief (kufr)?

What you mentioned is not disbelief (kufr), as it does not involve mockery of the Holy Qur’an or the legitimization of a sin. Fleeting thoughts that do not settle in the heart are not held against a Muslim. What is obligatory is: to keep away from sins and to hasten to repent from them.