Learn Spanish (Spain): Su hijo es joven.

Yes! The word su is very versatile. It can mean 'his', 'her', 'its', 'their', or 'your' (formal). You usually figure out exactly who the person belongs to from the context of the conversation. If it is not clear, a Spanish speaker might clarify by saying el hijo de él (the son of him) instead.

Does su match the gender of the parent or the son?

In Spanish, possessive words normally match the thing being owned, not the owner. However, su is special because it doesn't have separate masculine and feminine forms. It only changes for plurals (becoming sus if we were talking about multiple children). So it stays su regardless of who the parent is or whether the child is a boy or a girl.

Why do we use es instead of está for 'is young'? Age changes over time.

In Spanish, age and physical descriptions are treated as defining characteristics of a person, rather than temporary feelings or locations. Therefore, we use es (from the verb ser) instead of está (from the verb estar).

Would joven change to jovena if we were talking about a daughter?