It doesn't use any API (at least the YouTube plugin). So they are (according to their lawyers) not bound to any TOS. All it does is open the page (like a browser) and grab it and only show stuff to the user that's "relevant".
You can check it yourself, while it is not "open-source" or "free" in the usual sense its source is available.
Grayjay may not be bound to TOS but users of Grayjay are still accessing YouTube services in a way YouTube would prefer they didn't. OTOH videos are available without having to log in or having an account at all so I don't know if there's any implicit agreement between someone accessing a URL and the service provider.
True. And they might close your account if you login.
How I display, download or request data without an account and which browser or app I use to do it is still my choice. I'd guess if they could do anything about it, they would have half a year ago. The only way would be to DRM/widevine all videos and apparently they aren't ready for that yet. If they block my IP I'll just get a new one.
I wouldn't even be thinking about using a 3rd party app or blocking the ads if their service was reasonable. No way I will endure that, if they block it I'll just watch something else.
I don't think that's a problem: you can browse to YouTube's home page and search for and watch videos without logging in. Grayjay is just another user agent, as if it was another web browser.
I would assume these privacy claims would also include a ToS violation for the given platform?
And then of course the user has given Grayjay a lot of info so privacy?
Are they scraping the actual content too or just accessing it in some different way?