Learn Dutch: Wij hebben geen spiegel in huis. - We have no mirror in the house.

Geen is used to negate nouns that either have een (a/an) before them or don't have an article at all. Since you are saying "not a mirror", Dutch uses geen spiegel. Think of it as saying "We have no mirror."

Why is there no "the" (het) before huis?

In huis is a very common fixed phrase in Dutch meaning "inside the house" or "at home". If you said in het huis, it would sound like you are referring to a very specific physical building rather than the general concept of your home.

What is the difference between starting the sentence with wij instead of we?

Wij puts emphasis on the subject. By using wij, you are stressing that we (as opposed to someone else) don't have a mirror. If you were just making a casual statement without that contrast, you would normally use we.