Whose sister is she rather than it seems more correct, even though это implies a neutral/generic entity. You would use it for a dog, etc. but for a person, it is a pronoun like she that should be used. Or am I completely wrong? I am not a native speaker, I just think I know the rule. :p
It is чьё. The adjectival pro-words like мой, твой, наш, ваш, свой, какой, такой, чей all follow pretty much the same pattern with only a little variation.
Take a look at the full paradigm here if you are interested. You can decide for youself which of these you memorize right away and which can wait for later.
I thought that I was supposed to keep declined pronouns next to the noun it's connected to ("sister" is modified by "whose," so чья сестра это or это чья сестра?)
Or is that highly flexible as long, as the cases are right? (So, could I say "that horse is eating" as ета ест лошадь?)
The thing is, in Russian it is more idiomatic to either ask "Whose sister is she?" or "Whose sister is that?", not "Whose is that sister?"
To illustrate the difference, let's consider a couple declarative statements instead:
- This horse is mine.
- This book was amazing.
Here you have "mine" and "amazing" standing independently. You can say pretty much the same thing slightly different:
- This is my horse.
- This was an amazing book.
(here, you can replace "this" with "it", while "my" and "amazing" are connected to nouns)
Russian uses both structures, same as in English. I would argue that the second one is more common, and works better for a large number of adjectives.
It is only slightly more complicated with words like "this" (это) because both languages use "this" as a name for the object in question ("Take this") AND as an "adjective" ("Take this ball"). In Russian, only the "adjectival" это will follow the nouns's gender and case.