Well here a translation of the Italian song titles:
Cinema Paradiso: Profumo Di Limoni (Cinema Paradise: Smell of lemons)
La Califfa (don't really know if it's Italian, the word's not familiar to me)
Metti Una Sera A Cena (Doesn't really make much sense to me: Put an evening for/to supper. Or something like that)
Per Natale (For Christmas)
Lezione Di Musica (Music lesson)
Da Quel Sorriso Che Non Ride Più (From that smile that doesn't laugh anymore)
At least that's what I translated.

Great translations.... I can help you with the others:
- "Metti Una Sera A Cena" is an old italian movie (comedy) performed in 1969.
In common language it's seldom used, (e.g. dating someone) as a possible thing to do with the person you're talking to.
Literally, "metti" means "put", but in a phrase like that it means "imagine", describing a situation; so you can translate it "imagine an evening, having dinner
- La Califfa is also an old Italian movie and it mean "The Lady Caliph".
Sarah Brighman has a great version of this song. Click the link below to see. (The Italian lyrics are included!)
http://www.youtube.com/watch?v=FGzGwPUob3Y