Here, 'would' is correct as it is used for talking about things that often happened in the past. Here, he 'would' sing to himself when he was a boy. 
'Will' is used for talking about or predicting the future. Example: He will sing tomorrow.
Has' is used alongside the pronouns He / She / It and Who and singular nouns. Example: She has the pen I was looking for!
'Is' is used when the noun is singular. Example: How is your leg?