What is the correct manner of performing the Funeral Prayer that should be taught to someone who does not know it, especially if what the questioner previously learned was inaccurate?

The mistake the Imam made by reciting Al-Fatihah after every takbir except the first one does not invalidate the prayer, because repeating Al-Fatihah does not invalidate it, even if done intentionally.

However, if the Imam neglected to supplicate for the deceased, the prayer is invalid, because supplication is a pillar of the funeral prayer according to the four madhhabs. In this case, the prayer should be performed over the grave without exhuming it. This is the view of Abu Hanifah and Al-Shafi'i, a narration from Ahmad, and an analogy among the Malikis, based on the established fact that the Prophet, peace and blessings be upon him, prayed over the grave of the poor woman and did not exhume her.

A Muslim should seek deep understanding in matters of their religion, especially the individual obligations such as prayer and fasting.