How is the heart the place of intention, and is it sufficient for it to be a conversation with oneself without uttering it aloud, and is thinking of leaving the prayer due to an impediment, such as a doorbell ringing, considered an intention to leave it?

Intention (niyyah (definition)) is a firm resolve. If a worshipper hesitates about leaving the prayer, the intention becomes invalid according to some jurists, due to the condition of sustained intention, and hesitation contradicts firm resolve. Others hold that hesitation does not invalidate it, citing the hadith (definition) of Ibn Mas'ud and others, arguing that hesitation does not sever the firm intention. As for mere doubt about ablution (wudu') without hesitation to leave the prayer, it does not invalidate it. And the ringing of the doorbell and hearing it open is not considered an intention to leave the prayer.