It seems they used the most international-sounding word. I think you'd agree that Sud-Koreio is far more recognisable in the world than native-derived Daehano.
That was exactly what I was thinking. :) Though I use Manjaro (which is Arch based).
While I'm not entirely sure, just considering how each of them seems to be used, I think it's a similar distinction to Menschen vs Leute in German; one can be used to refer to humanity as an entire species and can be translated as 'humans' as well as people, and the other more specifically maps to the word 'people'.
In other words, you may be able to use homoj in a "People (humans in general)" sense but personoj would be the equivalent of 'persons' in English, referring more to a specific grouping of humans rather than all of humanity. I'd still like someone else to either confirm or deny this though, as this is just my best guess (well, not an unfounded guess, but that's neither here nor there…)
As not native English speaker i must say "I don't know". Multaj is an adjective, Multe is an adverb. I don't see difference between a lot and many, but I though it's not a mistake.
Yes, Polish. Maybe multaj is 'many' and multe: 'many of' And I haven't heard 'a lot ...'. Always 'a lot of'. But I really don't know is it difference or not.