并列的play the piano and violin可以省略冠词吗？——完全可以。比如高中英语外研版必修二（Module 3）中的 Beethoven（贝多芬）中就有这样一句：

By the time he was 14, Mozart had composed many pieces for the harpsichord, piano and violin, as well as for orchestras. 十四岁的时候，莫扎特已经为大键琴、钢琴、小提琴以及管弦乐队谱写了很多曲子。