Yes, it´s Bon Jovi´s hit. And yes it is Paul anka doing a swingjazz number of it that actually works very well. If you can bear that it is a bit cheesy Anka actually elevates the song to a whole new level and also manges to bring a sense of drama that suits the lyric very well.
Paul Anka sings esperanto? No, it`s just his italian version of "Put your head on my shoulder". I don`t know the year it was recorded, but I think it were in the late 60`s. Although his italian articulation sounds queer to me (it feels like he red the lyrics from a board) "Abbandonati Amore" is a very nice song and the "Hawaiian" melody is still the same as in the original recording!