Is the Fajr prayer a Sunnah or an obligatory (fard) prayer? Does it substitute for the Subh prayer? Is performing the Subh prayer at eight in the morning considered a make-up (qadaa') prayer?

The two rak'ahs of Fajr are a Sunnah (recommended) act, not obligatory, and they do not substitute for the obligatory Fajr prayer. Performing the Fajr prayer after sunrise is considered a make-up (qada'), not an on-time (ada') performance. A Muslim is obligated to perform the prayer at its prescribed time and in congregation.