Do you need to have long fingers for playing alto saxophone? I have small hands and can just reach an octave on the piano.
You don't need particularly long fingers to play alto saxophone. I can only reach an octave comfortably on piano, but I used to play tenor saxophone a bit, and this is bigger than alto. Besides, you don't stretch as far between thumb and little finger when playing the saxophone, as you do when playing octaves on piano, as the thumbs are placed behind the saxophone, approximately opposite the fingers.
I know that some saxophone teachers start children on soprano saxophone, which is smaller than alto, but all of my colleagues that teach saxophone start children on alto. So, this also shows that you don't need particularly big hands to play alto.