Learn Spanish (Latin America): Estamos construyendo una casa nueva.

The verb is construir (to build). Normally, to make the '-ing' form (the gerund) for an -ir verb, you add -iendo. But Spanish spelling rules do not allow an unaccented 'i' to sit between two vowels. To fix this, the 'i' changes to a 'y', making it construyendo. You will see this same change in other verbs, like leer becoming leyendo.

Why do we use estamos here instead of somos if both mean 'we are'?

When you want to say an action is happening right now (the present continuous tense), you always use the verb estar combined with the '-ing' word. Because building a house is an action in progress, we must use estamos, not somos.

Why doesn't the sentence say nosotros estamos?

The verb estamos already tells us exactly who is doing the action: 'we are'. In Spanish, you can usually leave out the subject pronoun (like nosotros) unless you specifically need to emphasize who is doing the action.

Why is it una casa nueva instead of una nueva casa?