I don’t have much experience in this field, so I can’t give satisfying answers to your questions. However, you said two things that I find very interesting:

> Also, there actually is Neanderthal DNA in the modern X chromosome.

> why is there no Neanderthal contribution to the modern Y chromosome?

I think both of these claims contradict the parent! I’m not sure which is correct, I’ve never looked into this before, and was simply trusting that bediger4000‘s assertion about the X chromosome was true. But it seems the opposite is true?