Learn French: Est-ce que votre famille a une ferme ?

Even though a family has multiple members, the word famille is a singular noun. Just like in English where you say "the family has" (not "the family have"), in French you use the singular form of avoir (to have), which is a.

Since this lesson is about the pronoun en, how would I answer "Yes, it has one"?

You would say Oui, elle en a une. The pronoun en replaces the noun ferme and goes right before the verb. When you specify a quantity like "one", you still put the number (une) at the very end of the sentence to show exactly how many.

If I want to replace votre famille with a pronoun in my answer, which one do I use?

You would use elle. Because famille is a feminine singular noun, you must replace it with the feminine singular pronoun elle (it/she), rather than a plural pronoun like ils or elles, even if you might use "they" in English.

Could I ask this question without using Est-ce que?

Yes! In everyday spoken French, you could simply say Votre famille a une ferme ? while raising your pitch at the end. You can also use inversion, but it gets a bit complicated when the subject is a noun (Votre famille a-t-elle une ferme ?), so Est-ce que is a perfectly safe and common choice here.