Is the questioner's act of donating money with the intention that it atone for gifts he took without right sufficient for him, or was it obligatory for him to donate to this specific center?

You mentioned that the center's administration gives gifts to the حلقه teacher to distribute among the four most diligent students, and that he knows his students best and is most aware of who among them is diligent. Although you sometimes omitted some verses when reciting to someone other than the teacher, which is a mistake, it does not negate diligence, nor does it imply that someone else is more deserving of the prize, especially since you mentioned that you were often diligent. Therefore, nothing is incumbent upon you. As for the charity you gave, there is no harm in it, and we hope that Allah Almighty will not deprive you of its reward.