"Do you know who the new principal is?"
Is it necessary to use both 誰 and 嗎 to form the question in this example?
I'm confused with that too. Isn't 谁 already a question word? Why is the 吗 needed afterwards?
Yes. 誰 is part of the inner question (新校长是誰). 吗 turns the outer sentence (你知道X) into a question. Without 吗 it would be a statement: "You know who the new principle is"
Yes, without "ma" the sentence becomes more of a statement. Like "you know who the new principal is". The "ma" can be interpreted like adding "right?" to the end of the sentence.
Because it is asking a yes or no question!
Do you know who the new principal is? 你知道新校長是誰嗎 Yes/no 知道/不知道
He is not asking who the new principal is (this would require some kind of description or name), so if he were asking this, it would be 呢), rather he is asking if the person knows who the new principal is. He either knows or he does not know, therefore it is 嗎.
"你們的新校長是誰(呢)?" would be fine, but the nuance is different.
I don't understand why the sentence needs the particle 吗，since 谁 already introduce a question. Exemple 这是谁的笔？ you don't say 这是谁的笔吗？
Do you know who is the new teacher? 你知道新的老師是誰嗎？
You know who is the new teacher 你知道新的老師是誰
Who is the new teacher? 新的老師是誰？