1. One of the stylistic origins of Hardcore Punk is "New Wave of British Heavy Metal".
Source:
https://en.wikipedia.org/wiki/Hardcore_punk
2. I was slightly wrong: All crossover thrash is both hardcore punk and thrash metal, but not all hardcore punk is crossover thrash. Either way, they're very similar. A band could call themselves one or the other, and pretty much no one would question it.
Source:
https://en.wikipedia.org/wiki/Hardcore_punk
3. I'm not sure how to interpret specifically what this means, but what I assume you may mean is that Noise Rock is not rock, and is in fact noise. Well, just like crossover thrash is a fusion genre, so is noise rock. Because of this, noise rock can be categorized as rock or noise, with some leaning more one way or the other.
Source:
https://en.wikipedia.org/wiki/Noise_rock