Learn Italian: L'adolescente protegge il proprio spazio personale. - The teenager protects his own personal space.

While you could grammatically use suo (il suo spazio), using proprio specifically means "his own". It can only be used when the owner is also the subject of the sentence (here, L'adolescente). It adds emphasis and removes any doubt about whose space is being protected.

Does proprio change its ending based on the teenager's gender?

No, it changes based on the thing being owned. Like all Italian possessive adjectives, proprio agrees with the noun it modifies. Since spazio is masculine and singular, we use the masculine singular form proprio, regardless of whether the teenager is a boy or a girl.

Normally the word spazio takes the article lo (lo spazio). Why is it il here?

Definite articles always agree with the word immediately following them. While you would say lo spazio because it starts with 's' + consonant, here the adjective proprio steps in between the article and the noun. Since proprio starts with a standard consonant ('p'), it takes the article il, resulting in il proprio spazio.

Is adolescente a masculine or feminine noun?