what you found recently is about wali, not about wakil. wakil is not always required, only in few cases. wakil represents, wali patronizes.
i think probably imam has done according his knowledge or even according to rulings of a mazhab , so probably he does not think himself sinful because they think they should just follow a mazhab.
i do not know rulings of mazhabs and i think this this way:
1) wali should be present in any nikah and wali should say whether he agree with nikah or not;
2) if bride is a matron, she should say whether she agree to the marriage or not and her opinion is stronger than opinion of her wali, even if the wali do not agree (she can marry or not marry regardless what wali thinks).
3) if bride is a virgin and she is shy she has not to say aloud that she is agree to the marriage and her opinion is stronger than opinion of her wali only if she does not agree (if she agree but wali does not, she cannot marry).
http://sunnah.com/tirmidhi/11/22 : Abu Musa narrated that : the Messenger of Allah said: "There is no marriage except with a Wali."
http://sunnah.com/tirmidhi/11/29 : Ibn Abbas narrated that: The Messenger of Allah said: "The matron has more right to herself than her Wali, and the virgin is to give permission for herself, and her silence is her permission."
http://sunnah.com/bukhari/67/72 : The Prophet (ﷺ) said, "A matron should not be given in marriage except after consulting her; and a virgin should not be given in marriage except after her permission." The people asked, "O Allah's Messenger (ﷺ)! How can we know her permission?" He said, "Her silence (indicates her permission).
answers to questions:
Was the Nikah valid? - yes, because you did no have knowledge and followed a person with more islamic knowledge, it is ok due to a quran ayat. additionally, even if wali was needed, as in my opinion, and as you think/afraid it might be, he could not force you to marry or not to marry, you just could follow your wali's opinion by yourself.
Have I committed a sin because I didn't know? - you probably did not make sin neither by your behavior, because, even if it was incorrect behviour, as soon as you did not know, you are not sinful for your that behaviour, and you are not probably sinful for not knowing that at first place because that is quite advanced topic and you could not know so much things, and also it is probably even a disagreement among different islamic scholars, so several different resulting opinions looks quite right do different scholars and you need to know quite much to have your own opinion.
What can I do or how can I repent? - i think you need not to repent or do anything else now. if you do not think it useless time spending, maybe you can make nikah second time just to make yourself more secure from sins?! but probably you should just ask allah to forgive you for that you did not asked for source texts for nikah?
What will make of our child if the Nikah was not valid? (Illegitimate?) - since i think your nikah is valid i do not answer.