I'm not 100% sure myself, but since no one else has replied in nearly a year I might as well share what I've gathered from the context: I believe nicht is meant to refer to singular or "definitive" things like "not", while nichts could be plural or even all things, like "nothing" in this case.
If that doesn't sound clear, I believe it's (essentially) like this:
nicht = not, nichts = nothing
Someone correct me if I'm wrong, of course.
In Danish and Norwegian, yes; in Modern German it doesn't though, instead the cognate is Mann. The mand in niemand was not borrowed from a North Germanic language, but it used to be nieman in Middle High German, but over the last 500-700~ years a [t] sound was added, and written with a d.
The difference is subtle in English, but it is there. If someone said, "Nothing is okay," I would then expect them to be able to give me a list of grievances or complaints about their life. "Nothing is normal" suggests things are not quite right, or they're a little strange, but it is not the same.
Also, generally I have not seen "normal" and "ok" used as synonyms in either language.