¿Cómo es tu primo? What's your cousin like?

Estoy and es

• estoy en el aeropuerto — where I am, so estar.
• ¿Cómo es tu primo? — what he's like in general, his looks and personality, so ser. That's why every answer uses es: Es alto y delgado, Es muy serio y un poco tímido, es muy amable. A question with está would mean something else: "how is he doing?". English makes the same split: "What's he like?" and "How is he?".

Tiene el pelo corto

• "He has short hair": Spanish uses tener, puts el before pelo and keeps pelo singular. The adjective comes after it: el pelo corto.
• con barba y gafas — "with a beard and glasses": no article after con here, while English needs "a".

¿Es rubio o moreno?

• "Is he blond or dark-haired?" — in Spanish both words are adjectives, and they go with ser.

¿Qué lleva hoy?

• llevar means "to wear" and "to have with you": "What's he wearing today?" The answer, Una chaqueta azul y una maleta grande, covers both: the jacket is on him, the suitcase is with him.

Lo veo, lo vas a ver

• ¡Ya lo veo! — "I see him now!": lo means "him" and comes before the verb (English puts "him" after it).
• ya lo vas a ver — "you'll see": here lo isn't "him" but "it" (that he's nice), and it comes before the whole vas a ver.

El chico de las gafas

• "The guy with the glasses", word for word "the guy of the glasses": the feature you recognize someone by is joined with de + article.

Mucha gente, ¿verdad?

• hay mucha gente — English "people" is plural, but gente is a feminine singular word, so it's mucha.
• ¿verdad? at the end of a sentence means "right?".