Learn Spanish (Latin America): ¿Cuántas personas viven en la casa?

The question word for "how much/many" changes to match the gender and number of the noun it belongs to. Since personas (people) is feminine and plural, we must use the feminine plural form cuántas. If you were asking about cars (autos, masculine plural), you would say cuántos.

Is personas always feminine, even if the people living there are men?

Yes! The word persona is always grammatically feminine in Spanish, no matter the actual gender of the person you are talking about. Even a group of only men is still referred to as las personas, which is why we use cuántas.

Why do we use the verb viven in this sentence?

Viven is the "they" form of the verb vivir (to live). Since you are asking about multiple personas, they act as the "they" of the sentence. Therefore, the verb needs to be in the third-person plural form.

Why isn't there a word for "do" in the Spanish question?

In English, we often use helper words like "do" or "does" to form questions. Spanish doesn't use these helper words at all. You simply state the question word, the subject, and the main verb directly: Cuántas personas viven....