If I miss rak'ahs of prayer, should I recite Al-Fatihah and a short surah when making them up? And what is the ruling on reciting a surah longer than what the Imam recited in the rak'ah in which I joined him, when completing the missed rak'ahs? And is that considered a reversal of the Quran?

The sayings of scholars regarding the prayer of a latecomer (masbuq) are: what the latecomer catches with the imam is the beginning of his (the latecomer's) prayer (which is the preponderant opinion), or the end of his prayer and he makes up what he missed, or he makes up for missed recitations and builds upon performed actions (according to the Malikis).

Based on the first madhhab, the completion of the prayer is explained in Fatwa no. 97602. If a latecomer misses one rak'ah, he makes up that rak'ah with Al-Fatiha and a surah, observing audibility (jahr) and inaudibility (israr). Reciting surahs in reverse order is disliked, and there is no mention regarding the latecomer specifically reversing the order of surahs relative to the imam's recitation. It does not concern the latecomer to know in which rak'ah he joined the imam. It is permissible for him to suffice with Al-Fatiha or Al-Fatiha and a surah in the rak'ah in which he joined the imam.