Praise be to Allah.
There is nothing wrong with the people of the mosque praying Taraweeh with twenty rak‘ahs, then if they want to pray however many rak‘ahs they want to after that – six or eight or ten, or more or less than that – they may do so. Then they may end with Witr prayer, provided that this number of rak‘ahs will not lead to them not being at ease whilst offering them.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on them) said:
The Prophet (blessings and peace of Allah be upon him) did not specify a particular number (of rak‘ahs) for qiyaam in Ramadan; rather he (blessings and peace of Allah be upon him) did not pray more than thirteen rak‘ahs (of qiyaam) in Ramadan or otherwise. But the rak‘ahs were very long, so when ‘Umar put the people together to pray behind Ubayy ibn Ka‘b, he used to lead them in praying twenty rak‘ahs (of Taraweeh), then three rak‘ahs of Witr, and he shortened the recitations in accordance with the increase in the number of rak‘ahs, because that was easier for the worshippers than making one rak‘ah very long. Then some of the earlier generations used to pray qiyaam with forty rak‘ahs and pray Witr with three, and others prayed qiyaam with thirty-six rak‘ahs and prayed Witr with three. All of that is permissible. So however qiyaam is done in Ramadan, in one of these ways, it is good; what is best varies according to the situation of the worshippers. If they are able to stand for a long time, then doing qiyaan with ten rak‘ahs and praying Witr with three, as the Prophet himself (blessings and peace of Allah be upon him) used to do in Ramadan and at other times, is preferable. But if they are not able to do that, then praying qiyaam with twenty rak‘ahs is best, and this is what most of the Muslims do, because it is in the middle between ten and forty. If they pray qiyaam with forty rak‘ahs or otherwise, that is permissible and there is nothing makrooh in any of that. This was stated by more than one of the leading scholars such as Ahmad and others. Whoever thinks that there is a specific number (of rak‘ahs) for qiyaam in Ramadan that has been narrated from the Prophet (blessings and peace of Allah be upon him), and one cannot do more or less than that, is mistaken.
End quote from Majmoo‘ al-Fataawa (22/272)
The scholars of the Standing Committee said:
Taraweeh prayer in the month of Ramadan is Sunnah mu’akkadah (a confirmed Sunnah) that was done by the Prophet (blessings and peace of Allah be upon him), who led his Companions in that prayer for many nights. Then he stopped leading them in that prayer, fearing lest it be made obligatory upon them. His companions did it during his lifetime and after his death (blessings and peace of Allah be upon him), and this practice has continued until today. With regard to the number of rak‘ahs, there is no proof of any specific number, and the scholars differed concerning it. Some of them think that it should be twenty-three; others think that it should be thirty-six; and others think that it should be more or less than that. At the time of ‘Umar, the Sahaabah prayed it with twenty-three rak‘ahs in the mosque of the Messenger of Allah (blessings and peace of Allah be upon him), but the Prophet never prayed more than eleven or thirteen rak‘ahs during Ramadan or at other times, and he did not set a specific number of rak‘ahs for people to do in Taraweeh and qiyaam al-layl. Rather he used to encourage people to pray qiyaam al-layl, especially in Ramadan.
Whoever makes the prayer lengthy may reduce the number of rak‘ahs, as the Prophet (blessings and peace of Allah be upon him) used to do. Whoever makes the prayer briefer out of compassion towards the people may increase the number of rak‘ahs, as the Sahaabah did at the time of ‘Umar.
There is nothing wrong with increasing the number of rak‘ahs in the last ten days of Ramadan and doing a different number than in the first twenty days, and dividing them into two halves, one half to be done at the beginning of the night and made brief on the basis that it is Taraweeh as done in the first twenty days, and the other half to be done at the end of the night and made lengthy, on the basis that it is Tahajjud. The Prophet (blessings and peace of Allah be upon him) used to pray Tahajjud in the last ten nights in a way that he did not do at other times.
End quote from Fataawa al-Lajnah ad-Daa’imah (6/82)
With regard to those who offer lengthy communal du‘aa’s, if that is at the time of Qunoot, in the last rak‘ah of Witr, then this is prescribed and is good, and there is nothing wrong with it.
If that is done after the end of the prayer, as we understand from the question, then it is an innovation (bid‘ah); it was not the practice of the Sahaabah and early generations, and none of the leading scholars – as far as we know – regarded it as mustahabb. So what must be done is to object to that and teach them the Sunnah, and inform them that this kind of du‘aa’ comes under the heading of innovations that have been introduced into the religion. Whoever wants to converse with his Lord, remember Him (dhikr) and call upon Him (du‘aa’), let him do that individually, not in a group, and in a soft voice. But those who seek to convey this message must do so with wisdom and beautiful preaching.
The scholars of the Standing Committee were asked:
There are some imams of mosques who, after each four rak‘ahs of Taraweeh prayer, say a communal du‘aa’, such as saying “Allaahumma innaka ‘afuwwun tuhibb al-‘afwa fa‘affu ‘anni (O Allaah, You are forgiving and You love forgiveness, so forgive me)”; what is the ruling on that?
The committee replied:
It is not permissible to offer a communal du‘aa’ after every four rak‘ahs, because this is an innovation (bid‘ah) for which there is no evidence in the Qur’an and Sunnah.
End quote from Fataawa al-Lajnah ad-Daa’imah (6/85)
You should carry on praying with them and calling them to the Sunnah, but you should not join them in this du‘aa’; rather you should sit and wait for the prayer so that you may pray with them, and concentrate on reading Qur’an or offering supplication (du‘aa’) and remembering Allah (dhikr), each one doing so by himself, and objecting in your hearts and verbally to any action that is contrary to the Sunnah and anything that is introduced into the religion of Allah.
If they persist in doing this innovation, and you are able to pray in another mosque where the people are keen to follow the Sunnah and avoid bid‘ah, that is preferable.
It is not part of the Prophet’s Sunnah to offer a particular du‘aa’ after completing a reading of the Qur’an; there is no report to that effect from the Companions of the Prophet (blessings and peace of Allah be upon him) or the well-known imams (leading scholars).
So there is no basis for offering a du‘aa’ after completing the Qur’an in the prayer.
Outside of prayer, there is a proven report from Anas ibn Maalik (may Allah be pleased with him).
It is not known from the Sahaabah or the early generations who came after them that they used to gather in the mosque to offer du‘aa’ after completing the Qur’an in Taraweeh, or in the prayer or otherwise.
But if the du‘aa’ after completing the Qur’an is proven to be from Anas (may Allah be pleased with him) or anyone else among the Taabi‘een, then there is nothing wrong with that in general, so long as it is not done communally or as a persistent practice, with a specific wording.
The scholars of the Standing Committee said:
Offering du‘aa’ after completing the Qur’an is prescribed, but it should not be done persistently and one should not adhere to a specific wording as if it is a Sunnah to be followed, because that is not proven from the Prophet (blessings and peace of Allah be upon him); rather it was done by some of the Sahaabah (may Allah be pleased with them).
End quote from Fataawa al-Lajnah ad-Daa’imah (2/480)
And Allah knows best.