Classical Music: Who wrote a set of piano pieces, each named for a month of theyear?

Questions

Although he breezed through the Paris Conservatory's entrance exams, who was refused admission because he was age 7?

Grieg's Peer Gynt was originally incidental music to a play of the same name. Who wrote the play?

In the music of J.S. Bach, one can find evidence of...?

In 1705, J.S. Bach was exposed to a composer who influenced him greatly. Who was he?

Leonard Bernstein's last minute conducting debut with the N.Y. Philharmonic in 1943 launched his career. Who was he filling in for ?