Re: He is studying/learning to play the piano.
"Studying" to play the piano sounds as if the person is reading books about the piano, about the theory of playing the piano, how a piano works etc. It doesn't sound as if the person is actually sitting at a piano, playing music.
Having said that, if someone attends music college, they would say "I'm studying piano at Juilliard". They wouldn't say "I'm studying to play the piano at Juilliard".
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.