Will the teacher incur sin due to her colleagues' and director's lack of commitment to school attendance, which affects the flow of her classes and the students' concentration, knowing that she is keen to perform her duty fully and signs the attendance register without writing the time?

What you mentioned about the director and her colleagues' absence and negligence is a dereliction of their religious and professional responsibility. A severe warning has been reported concerning those entrusted with authority who do not act justly, as the Prophet (peace be upon him) said: "There is no ruler over ten except that he will be brought forth chained on the Day of Resurrection until justice releases him or injustice destroys him." As for you, may Allah reward you with goodness for your commitment. There is no sin upon you as long as you are not responsible for the signing and have not fallen short in your duty, and you have offered advice. And "O you who have believed, upon you is [the responsibility for] yourselves. Those who have gone astray will not harm you when you have been guided."