What is the ruling on one who conveys information based on their understanding, then discovers its error? And is one sinful if they do not give students full marks for their efforts to avoid accountability from the department?

A servant is not held accountable for mistakes, as Allah Almighty says: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts intended." This includes a teacher's error in teaching, for which there is no sin upon him. However, he must correct the erroneous information when he becomes aware of it, as Imam Malik and Abu al-Fadl al-Jawhari did. If the student deserves a full mark based on their effort, it must be given to them, and deducting it would be an injustice to them.