Here ya go; this should answer both of your questions! :O)
https://community.ricksteves.com/travel-forum/italy/train-tix-florence-to-cinque-terre
l'll mention that the Cinque Terre ("5 lands") is not a singular place but a collection of 5 villages strung along a shared rail line. They are only a few minutes apart but you would need a new ticket for each ride (and you must validate them before boarding!) or buy a 1-day Treno card. That card covers almost all the trains (not any high-speed trains) running between La Spezia to the south and Levanto to the north; the 5 villages - Monterosso, Vernazza, Corniglia, Manarola and Riomaggore) - are in between. The Treno card also covers access to any open segments of the Sentiero Azzuro ("Blue Path") trail system. There are currently only 2 of those open this season. The Treno card needs only to be validated before boarding your first train into the region.
http://www.parconazionale5terre.it/Ecinque-terre-card.php