If you use "search" you will find a lot on your topics. From Villefranche you can walk from the tender pier to the train station or the bus stop. The train line spans the entire Riviera coast and you can be in Monte Carlo in about 20 min or in Nice in about 10. However, keep in mind that you might wait 45 min for the train. The bus lines also go both directions but they do make more stops and are somewhat slower. I do not believe round trip tickets offer any real savings, but perhaps this has changed. As to your route, keep in mind that Nice is about 10 min (on the train) West of Villefranche and Monte Carlo is 20 min East. However, the same train line covers both cities and you could even go as far as Menton (to the East) or Cannes (to the West) with no problem. There is only one train station in Villefranche. You get there by walking off the tender pier, than turning towards your right and walking (keeping the water on your right) until you see the steps (on your left) that lead up to the train station. The trains going towards your right (as you face up the hill) are heading towards Monte Carlo and the ones going towards your left are going towards Nice...Anbibes, and Cannes.
As to Palermo (I never liked this city) my favorite place is the Catacombe Cappuccini. Google the place and read the info...its really macabre but quite interesting. You can get there from the pier by using public buses or a taxi.