There are three answers to this question –

1. The study of pre-existing works from the canon literature in order to facilitate the understanding of music construction, form, aesthetic, and ideals.
2. The study of the basic craft and idiomatic writing for instruments and voice.  
3. The analysis and fostering of the student’s works.

While it is ideal, yes.  If not, one can learn composition by ear.

A student can be age 5 to age 105!