What is the difference between She has never been late for class and neither have I. and She has never been late for class and nor have I. ?Feel free to just provide example sentences.

Could also be:
Neither she nor I have ever been late for class.

The most common for your sentence would be “Neither of us has ever been late to class.”

While w-silent’s answer is grammatically correct, you will never hear anyone speak like that, your sentence is more natural.

People will use either/or very often, but typically no one uses neither/nor in everyday speaking. Because it sounds strange to have so many negatives. So we say “I don’t like —— or ——. I also don’t like ——. [I don’t like —— either.]

And you can use nor alone as in:
A: I don’t like ——.
B: Nor do I. [but not very common]

These would be more common:
Neither do I.
Me neither.