Is a Muslim considered an unbeliever if he misses Fajr prayer after waking up to the alarm before the Adhan and then goes back to sleep until the prayer time has ended, or if he wakes up to the Adhan and then is overcome by sleep until he misses the prayer? What is the ruling on delaying the 'Isha prayer for a man, and is a Muslim considered an unbeliever by intentionally delaying any obligatory prayer?

There is no sin upon one who sleeps before the prayer time enters. Rather, sin is incurred by one who sleeps after the time has entered if he predominantly believes that he will not wake up before the prayer time expires, and he has not taken measures to ensure waking up. The optional time for the 'Isha prayer extends to one-third or half of the night, after which it becomes a time of necessity until the emergence of dawn.