Does it really need the a here? Would it not go without it: We are mopping house or better yet: We are mopping the house
Either "a house" or "the house" should be accepted. "Mopping house" sounds like it might be possible in some dialects - there are set phrases like "keeping house", for example, but I've never heard "mopping house".
In the tips it talks about SVO so why is it not "Tunapiga nyumba deki"?
"Deki" is part of the verb in this case and "nyumba" is the object.
deki ya nyumba?