People in India used to recite Qur'an over their food and make Du'a (saying al-Fatiha); Is it permissible in light of Islam? Please answer.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Reciting any part of the Quran or Soorah Al-Faatihah, or Supplicating over foods or graves or marriage ceremonies, is not proved from the Prophet his companions or the pious predecessors. If these acts were good, no doubt, they would have performed them before us.

What is proved from the Prophet is sufficient for Muslims, especially in the matters of reciting the Quran and Supplicating (making Du'aa’), since these matters relate to forms of worship. As you know, there can be no opinions in this matter. We are obliged to restrict ourselves to these forms and manners of worship, which are proved from the Prophet . We will mention here what is proved from the Prophet in the matter of eating, drinking, etc.

1. Imams Abu Daawood, At-Tirmithi and others narrated from ‘Aa’ishah that the Prophet said: When one of you eats, he should mention Allah's name; if he forgets to mention Allah's name at the beginning, he should say:

"بِسْمِ اللَّهِ فِي أَوَّلِهِ وَآخِرِهِ"
"In the name of Allah at the beginning and at the end of it."

Shaykh Al-Albaani said in his famous book Saheeh Al-Jaami’ As-Sagheer: “This Hadeeth is sound.”

2. Imams Abu Daawood, At-Tirmithi, Ibn Maajah and Ahmad narrated from Ibn ‘Abbaas that the Prophet said: When one of you eats food, he should say:
اللّهُـمَّ بارِكْ لَنا فيهِ وَأَطْـعِمْنا خَـيْراً مِنْـه. "
“O Allah! Bless us in it and give us food (or nourishment) better than it.” When he is given milk to drink he should say:
اللّهُـمَّ بارِكْ لَنا فيهِ وَزِدْنا مِنْه.
"O Allah! Bless us in it and give us more of it.”; for no food or drink satisfies like milk.

3. Imams Abu Daawood, At-Tirmithi, and Ibn Maajah reported from Mu’aadh ibn Anas that the Prophet said: "When one of you eats food and says:
"اَلْحَمْدُ لِلَّهِ الَّذِي أَطْعَمَنِي هَذَا وَرَزَقَنِيهِ مِنْ غَيْرِ حَوْلِ مِنِّي وَلاَ قُوَّةٍ"
“All praise is due for Allah who fed me this and provided it for me without any might nor power from myself”; Allah forgives his past sins.”

Imam At-Tirmithi said: “This Hadeeth is good.” Shaykh Al-Albani said: “This is a sound Hadeeth.”

4. Imam Al-Bukhari reported from Abu Umamah that he said: “Whenever the Prophet finished his meals (or when his dining sheet was taken away), he used to say. “Praise be to Allah Who has satisfied our needs and quenched our thirst. Your favor cannot by compensated or denied." Once he said, “Praise be to You, O our Lord! Your favor cannot be compensated, nor can it be left, nor can it be dispensed with, O our Lord!”
"الْحَمْدُ لِلَّهِ حَمْداً كَثِيراً طَيِّباً مُبَارَكاً فِيهِ غَيْرَ مَكْفِيِّ وَلاَ مُوَدَّعٍ وَلاَ مُسْتَغْنيِّ عَنْهُ رَبُّنَا"

“May Allah be praised with an abundant beautiful blessed praise, a never-ending praise, a praise which we will never bid farewell to and an indispensable praise, He is our Lord.”

5. The supplication narrated by Imam An-Nawawi in his book of supplications "Al-Adhkaar" is that whenever food was presented to the Prophet he used to say:
"الَّلهُمَّ بَارِكْ لَنَا فِيمَا رَزَقْتَنَا، وَقِنَا عَذَابَ النَّارِ"
“O Allah! Bless us in the food which you have granted us and protect us from Hellfire.” This Hadeeth is not authentic.

These are some details presented here. Finally, the general rule is that a Muslim should perform only what is proved from the Prophet concerning supplications, recitations etc.

Allah knows best.