After a Qur'an recitation class or lesson is it Sunnah for all the people present in the class to raise their hands and make Du'a asking Allah (S.W.T) for general things of this life and Akhira after a gathering? Can the person who is giving the lecture say this Du'a Subhanka Allah humma wa bihamdika nashhadu an la ilaha illa anta wa nastagfiruka wa natoob ilaik - for all the persons present in the Qur'an lesson or should it be .....wa astagfiruka wa atoob ilaik ..... as per the Sunnah of our Prophet (S.A.W)?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Asking Allah in groups after reading the Qur'an or after studying it is an innovation according to many scholars. Imam Malik said about a group of people who get together to read the Qur'an: 'There is no harm in getting together for the Qur'an but it is disliked for them to make Dua' after finishing it'.
Getting together to study the Qur'an or read it is desirable as reported by Muslim that the Prophet said: "those persons who assemble in one of the houses of Allah (mosques), recite the Book of Allah and learn and teach the Qur'an (among themselves). There will descend upon them tranquillity, mercy will cover them, the angels will surround them and Allah will mention them in the presence of those near Him. He who is slow-paced in doing good deeds, his (long) descent does not make him go ahead. [Reported by Imam Muslim].
As for making Du'a after reading the Qur'an or studying it, it is an innovation which should not be done.
As for changing "Astaghfiruka" to "Nastaghfrouk", you are asked to say the words of Du'a that is narrated as they were narrated without changing any word or adding to it. The evidence for this is the Hadith reported by Al Bukhari and Muslim from Al Bara that he said: "Allah's Apostle said to me, "When you want to go to bed, perform ablution as you do for prayer, then lie down on your right side and say: 'Allahumma aslamtu Nafsi Ilaika wa wajjahtu wajhi ilaika, wa fauwadtu amri ilaika wa aljatu zahri ilaika, raghbatan wa rahbatan ilaika, lamalja'a wa la manna minka illa ilaika. Amantu bikitabi kalladhi anzalta wa bi nabiyyikal-ladhi arsalta'. If you should die then (after reciting this) you will die on the religion of Islam (i.e., as a Muslim); so let these words be the last you say (before going to bed)." While I was memorizing it, I said, "Wa birasiulikal-ladhi arsalta (in Your Apostle whom You have sent)." The Prophet said, "No, but say: Wa binabiyyi-kalladhi arsalta (in Your Prophet whom You have sent)."
Imam Ibn Hajar said: "This is an evidence that the words of Dhikr (Du'a from the Prophet) should be kept intact because they have an essence peculiar to them. So, one must say them as they were reported. The reward might be complete only with these letters. So the Dhikr should be said as revealed'.
Allah knows best.