I said "It's here she lives" (so, spelled correctly) and it was marked wrong. The "that" that they require "It's here that she lives" is definitely not necessary in English, and is in fact extraneous, though not actually incorrect. If I were editing a document I would chop the "that" out.
If I have learnt one thing during this course, that'll be the French don't like to be repetitive or redundant the way they talk.
They do their best not to repeat the focus point of the talk twice in a sentence or in a conversation.
And this is how I understand your explanation :)
It's just the wrong word order. "She lives here" is what you would say. This sentence seems to be trying to stress the HERE though. It's HERE she lives. Instead of over there-- where you thought she lived.
I don't think Duo is teaching a Yoda dialect, which is what Here she lives sounds like.
I see your logic. After thinking about it, I think is because your examples are "set phrases." "Here we are" could mean "We are here," or it could mean we have just found something we were looking for. For example, 2 people searching for lost keys suddenly find them and say "Here we are/go."
"There she goes," however, does not mean "She goes there." For example, if I have been looking for someone and suddenly see her walking away, I might say "There she goes," or if she's walking toward me, "Here she comes."
It can also be used as an idiom, for example, a friend has come up with crazy ideas in the past, and now she has a new one that she's going to try, I might turn to another friend and say "There she goes," with an unspoken addition to the phrase being: again, off on one of her crazy ideas.