Views Taxonomy selection and display
This can be achieved using following approach.


Create a content type for example "Favorite song" and add a field of "Term reference" type into this content type where widget will be "Check boxes/radio buttons" and select the vocabulary of songs for options.
Give permission to users to add/edit content "Favorite song",then while adding user will select their favorite songs from the list of songs.
Again to view/edit favorite song list of a user you can find the correct node by author of the node.


Hope it will help.