Learn Italian: Il suo figliastro studia all'estero.

You are right that standard, unmodified singular family members drop the article (like suo padre). However, altered nouns are an exception to this rule. Because figliastro is formed by adding a suffix to the base word figlio, it requires the definite article.

How do we know il suo means 'her' here, rather than 'his'?

In isolation, we don't! Italian possessives agree in gender and number with the noun being possessed, not the owner. Since figliastro is masculine singular, the possessive must be il suo whether the parent is a man or a woman. The provided translation uses 'her' based on outside context.

What does the suffix -astro mean in figliastro?

The suffix -astro generally gives an altered, 'lesser', or sometimes pejorative shade to a word in Italian. However, when attached to family terms like figlio (son) or fratello (brother), it acts just like the English prefix 'step-', creating figliastro (stepson) or fratellastro (stepbrother).

Why do we use all' in the phrase all'estero?