A lot of lit from the Black liberation movement uses "Black". I'd say that the majority of people I've seen capitalise Black have been Black themselves. That isn't to say it represents a majority of Black people, but also I don't think "what do the majority of this group think" is the best metric for determining what's right—e.g. a significant amount of women are figureheads of the anti-abortion movement, but that doesn't mean that they're right or not misogynistic.
I wasn’t sure if I should use “themself” or “themselves”
Different people who use they/them will have different preferences. If you don't know the person's preference, I doubt they'd care about which you go with, and if they did, they can reach out to you after the fact and ask you to change it or to use a different option going forward in the future.
If they don't think animals should be kept in captivity, they shouldn't keep a pet. Pets are, by definition, captive animals. If I befriended a pigeon by feeding it, it wouldn't become my pet; it only would if I captured it.