I think "sore wa nanimonai" does not make sense; it literally means "It is that there is nothing". "Nani-mo" and "Nan-de-mo" have a larger difference than it looks like. I can understand "nani demo arimasen" but it is not "nani demo " but "nan demo". It should be ""nandemo arimasen"

I think the difference between them is that the second one is more formal, but you could also say "dou itashimashite"