'Whose children are these/those' implies that the children are to hand, physically near the speaker, whereas in 'whose children are they', this is not the case. I don't know whether Russian makes this distinction or not; if it doesn't, 'they' should be accepted; if it does, perhaps not.
I thought I understood that distinction, but I don’t understand why it’s это here. Here it doesn’t seem to be acting as a standalone particle or pronoun (as in e.g. Это дети, These are children); it seems to be modifying a noun, these children, это дети, so why wouldn’t it be the inflected form эти?
It seems to me that it's just a misconception of word order. In the Russian sentence, you could probably switch the position of «это» to pretty much any other position, and it would have the same meaning. Think of it this way: "These are whose children, yours?" «Это чьи дети, твои/ваши?»
I'm having trouble understanding the pronunciation of the first two words, which seem to blend together somewhat to me, like "Чьи это", sounds like "chi-yi, a eto". I have no clue what's going on here either...why the soft sign ofter the "ч"? I thought "ч" was always a soft consonant, so I'm not clear on what effect it has when you put a soft sign after it. And then where is that intermediate sound coming from? Like why doesn't it just sound like i...eto"? What is that sound in the middle?