Learning music by ear has no particular term. It is a talent or a gift. Some of the prodigy students I met in Melbourne School of Music have this capability - they listen repetitively to music [at home] and they try to play the notes on piano or guitar. Wish I had that too. =)
Sometimes people who are self-taught and play by ear rather than by music notation are called natural musicians.
No clue but that's the only way I fan play piano. Sheet music is too confusing and I'm less likely to forget.
Do you mean the Suzuki method of teaching music by ear to children too young to read score yet?
I don't think there is a term for that. It's just learning music by ear.
