What should I do if I prayed behind an Imam and there was a child to his right, knowing that I do not know if the child had reached the age of seven, and I do not remember which prayer it was? And what should I do if the same situation happens again?

What you did, by standing with the child behind the Imam, is correct, whether the child was discerning (mumayyiz) or had not yet reached the age of seven. The important thing is his discernment. The Hadith of Anas ibn Malik indicates that the Prophet, peace and blessings be upon him, led Anas and an orphan in prayer behind him, and the old woman was behind them. This indicates the validity of the discerning child's prayer, that he has a position in the row, and that two people form a row behind the Imam.