You need a pass to hike the lower coastal trail - the SVA2 Sentiero Azzurro (Blue Path) route - between Monterosso and Vernazza, and Vernazza and Corniglia.
http://www.parconazionale5terre.it/Eiti_dettaglio.php?id_iti=3577
http://www.parconazionale5terre.it/Eiti_dettaglio.php?id_iti=3578
Via dell'Amore is largely closed and has been so for quite a number of years now:
http://www.parconazionale5terre.it/Eiti_dettaglio.php?id_iti=3575
The Cinque Terre Treno MS Card pass would cover both the CT regional trains and hiking fees for your itinerary. It would not cover trains to La Spezia from outside of the region, such as from Florence, nor a return from L.S. to Florence or other locations outside of the region.
http://www.parconazionale5terre.it/page.php?id=158
A one-day card doesn't have 24-hour validity so if you validated it the morning of arrival, it would expire at midnight of that same day.