"The school is behind our home."
Yeah, you don't need it, speaking casually. A lot of people drop the first one, too.
I agree - I left the second one out. I think leaving the first one out is possible too but is a little colloquial right?
Both 的s are unnecessary, especially the second. This does not reflect common usage.
是 is not only for nouns. 是在 is not bad construction.
Obvious this course want to teach how to use 在, but depending on the context you can substitute it with 是在. I can elaborate if anyone is curious.
About “A 是 B 的后面”: Without context, a sentence like this does not make much sense. It is like saying “A is the back of B”. Rather, we should say “(在) B 的后面是 A” (Behind B, there is A.). I can't tell why the 在 before B is optional, but that's it.
It strikes me that 学校是在我们家的后面 is a strong affirmation, as though you are arguing with someone about the location of the school. Is there another usage for this structure?
Sorry, not sure where you got this impression, but you can read my another comment: https://forum.duolingo.com/comment/25359745$comment_id=31106575