Will one be rewarded for having intended to recite a portion of the Quran after Fajr, but then died before doing so, or will one be rewarded for completing the recitation of the entire Quran, which he was accustomed to finishing every Ramadan?

The intention to perform acts of obedience is rewarded; thus, whoever intends to do good but is unable to, or was performing an act of obedience and was prevented from completing it, will receive its full reward. This is supported by the Prophet's (peace be upon him) saying: "Indeed, Allah has recorded good deeds and evil deeds, and then He clarified that. So, whoever intended to do a good deed but did not do it, Allah records it for him as a complete good deed." An example of this is someone who intended to complete the recitation of the Quran in Ramadan, but then died before finishing it; the reward for completing the entire Quran will be written for him due to his intention.