I don't agree, I think English speakers would say "We are moving into the house." "Move in" is a stand-alone phrase. You would say, "I'm moving in with him," or "We're moving in next Wednesday." But if you want to talk about the place where you're moving in, you would say "moving into" that place. Not "moving in" that place, and definitely not "moving in into" that place.
It's not considered wrong, it's just that the course creators didn't enter the second sentence as another valid translation. Each option has to be entered manually. This should be reported.
My personal preference would be for your second sentence, not because it's better English, but because it's closer to the Hungarian. "We also" parallels "Mi is."
It also makes it clearer what the "too" (or "also") applies to. I assume that in this scenario, we are moving into a house that other people are also moving into. Putting "too" at the end makes it ambiguous. It's possible someone is saying, "We've already moved into this house. Are we moving into that house, too?" I guess it depends on how much money you have. :) So the Hungarian rule of putting "is" after whatever it modifies makes perfect sense to me!
But I still don't like "are we moving in that house?" We move INTO a house. Or, we "move in," period. So you can ask someone, "When are you moving in?" Or you might ask, "When are you moving into the new house?"
I speak American English. People speaking other varieties of English might differ...
That's funny. I think they can add alternative translations to a list of accepted answers, but they can't remove or change something that is already there. So if many correct answers are added, then it's less likely that a valid translation will be rejected. On the other hand, if someone enters an invalid translation that just happens to be in the list, that translation will unfortunately be accepted. I don't think that can be changed.
I put "to that house" instead of "into that house" and both are correct
For me, "into that house" means the movement stops "in" the house, while "to that house" means the movement stops "at" the house (you are next to it but still outside it).
"to that house" would be ahhoz a házhoz, I think.
In the context of moving house, the word "into" isn't necessary. I would also argue that the word "to" is more often used. Consider the following conversation between Janet and John:- Janet: "We are moving house." John: "Oh, really, where are you moving to?" Janet: "We're moving to that white house by the windmill." Just as John doesn't say, where are you moving into, (and that would sound odd), so Janet doesn't need to say that she's moving into the white house by the windmill. Saying that she's moving to it is sufficient.