2-He was a shy boy, who loved the books and the music. (Incorrecto)

    Corrección: He was a shy boy who loved books and music. 

3-He studied aeronautical engineering in the college. (Incorrecto)

    Corrección: He studied aeronautical engineering in college. (No se usa "the" antes de "college" en este contexto).

4-He was the first man who set foot on moon. (Incorrecto)

   Corrección: He was the first man who set foot on the moon

5-His famous words were heard by people all over the world. (Correcto)

6-Before becoming a astronaut, he worked for the US Navy. (Incorrecto)

    Corrección: Before becoming an astronaut, he worked for the US Navy.

7-After 1994, he refused to give the autographs. (Incorrecto, aunque depende del contexto)

   Corrección: After 1994, he refused to give autographs. (Si se refiere a autógrafos en general, no se usa "the").

    Alternativa (si se refiere a autógrafos específicos): After 1994, he refused to give the autographs he was asked for.

8-In 2005, he was involved in a lawsuit with an ex-barber, who tried to sell some of the Armstrong's hair. (Incorrecto)

   Corrección: In 2005, he was involved in a lawsuit with an ex-barber who tried to sell some of Armstrong's hair.

2.- shy boy, books and the music

3.- correct

4.- on the moon

5.- correct

6.-an astronaut

7.- autographs

8.- Armstrong's hair

2-He was a shy boy who loved books and music

3-he studied aeronautical engineering in college

4-He was the first man who set foot on the moon

5-His famous words were heard by people all over the world

6-before becoming an astronaut, he worked for the US Navy

7-after 1994, he refused to give autographs he was asked for