It is Sunnah for the guest to offer supplication for his host after he has finished eating, because of the report narrated by Muslim (2042) from ‘Abdullah ibn Busr, who said: The Messenger of Allah (blessings and peace of Allah be upon him) came to my father and we offered him some food and a mixture of dates, dried yoghurt and ghee. Then some dates were brought and he started eating them, putting the stones between his fingers and holding his forefinger and middle finger together. Then some drink was brought and he drank it, then he passed it to the one who was on his right. My father said, taking hold of the reins of his riding-animal: Pray to Allah for us. He said: “O Allah, bless them in that which You have provided for them, and forgive them and have mercy on them.”
An-Nawawi (may Allah have mercy on him) said:
This indicates that it is mustahabb (encouraged) for the guest to pray for increased provision, forgiveness and mercy (for his host). In this supplication (du‘aa’), the Prophet (blessings and peace of Allah be upon him) mentioned the good things of both this world and the Hereafter.
Abu Dawood (3854) narrated from Anas that the Prophet (blessings and peace of Allah be upon him) came to Sa‘d ibn ‘Ubaadah and he brought some bread and olive oil and he ate, then the Prophet (blessings and peace of Allah be upon him) said: “May fasting people break their fast with you, may the righteous eat your food, and may the angels send blessings upon you.”
But the supplication that is offered after eating, or before, or in any other situation, should only be supplication that a person offers by himself, and not in the communal form mentioned in the question.
The scholars of the Standing Committee were asked:
There is a person whose habit is to give food to a group of people every Friday, and when the food is finished, they do not leave their places or their seats; rather they wait for one of them, who is appointed by the one who has given the food, to pray to Allah to cause the reward for that food to reach their deceased family members and relatives. During that supplication, the one who is asking of Allah raises his hands, as do the other people present, and they say Ameen. Is this supplication during which the group raises their hands after eating permissible or not?
Communal supplication in the manner mentioned after eating is something for which there is no basis in Islam. Therefore what they must do is stop doing that, because it is an innovation; they should be content with that which is mentioned in the Sunnah of offering supplication and asking for blessing (barakah) for the one who gave the food, and the like. Each person should offer supplication of his own. It is narrated in the Sunnah that one may say “Allahummah baarik lahum fima razaqtahum waghfir lahum warhamhum (O Allah, bless the provision that You have granted to them, forgive them and have mercy on them), and “Aftara ‘indakum as-saa’imoona wa akala ta‘aamakum al-abraaru wa sallat ‘alaykum al-malaa’ikah (May fasting people break their fast at your table, may the righteous eat your food, and may the angels send blessings upon you).”
End quote from Fataawa al-Lajnah ad-Daa’imah, 24/189-190
Reciting al-Faatihah and specific du‘aa’s before eating, and claiming that the Prophet (blessings and peace of Allah be upon him) recited this supplication before eating, is an innovation for which we know of no basis in Islam. It is not known from his Sunnah that he (blessings and peace of Allah be upon him) used to raise his hands to offer supplication or recite al-Faatihah before or after eating. Therefore what you must do is give up this innovation and be content with that which is narrated in the saheeh Sunnah, and rely on the books of well-known scholars who are able to distinguish sound (saheeh) hadeeths from those that are weak, and what is Sunnah from what is innovated.
You should also advise people to do likewise, and warn them against innovations that have been introduced into Islam.
And Allah knows best.