First question: Here is an intro to Italian bus travel. Fasten your seatbelt before reading. http://italyexplained.com/bus-travel-in-italy/
This site is a consolidator that simplifies your schedule & ticket choices, but they make a markup on the prices https://www.goeuro.com/buses/italy
According to the Trenitalia website, you can take a train from Rome but then you have to transfer to a bus in Isernia, which is quite out of the way. It looks like the travel time is between 3.5 and 4 hours one way.
Second question: It's about 7 hours by train from Rome to Zurich. Depending whether you can get from Castel di Sangro back to Rome early enough in the morning to catch a fast train to Zurich, it may be doable. I think flying Rome-Zurich would be easier, though.