What is the ruling on my saying: "By God, I don't know," when I know that my friend was the one who called the teacher, and what are the consequences of that, and am I obligated to inform the teacher of the truth?

One must repent from lying by ceasing it, regretting having done it, and resolving never to return to it. It is not necessary to inform the woman about the lie told to her, because the benefit lies in concealment and suffices with repentance.