I'll take a stab at some of your questions, Sarah -
Trains: please use the Trenitalia website for exploring your rail options but depending on the your preferences from Florence (Firenze SM Novella station) you'll be changing trains in La Spezia Centrale station OR have two changes, one in Pisa and another in La Spezia OR a change in Firenze Campo di Marte and La Spezia.
https://www.trenitalia.com/en.html
Food: Corniglia is tiny but there are two little markets for picking up some provisions: google up Lisa Market and A Butiega, both seeing high marks on google reviews. If you're coming into Corniglia later in the evening, you might want to have purchased some items in Florence to hold you until the next morning if not planning to eat out.
I am planning to hike North 1 day and South another. With the entire
trail being 11km...
There are MANY trails in the park but I'm guessing your plan is to cover the very popular Sentiero Azzurro (Blue Path) route? Understand that of its 4 sections, the one between Corniglia and Manarola has been closed to landslide damage for many years, and while the Via Dell'Amore section between Manarola and Riomaggiore is open again, access requires a reserved, timed-entry ticket in addition to the Trekking or Treno card required to access any section of the"Blue" https://www.parconazionale5terre.it/Ecinque-terre-card.php.
Unless weather intervenes (they close the trails when rain makes them unsafe) you shouldn't have issues from Corniglia> Vernazza> Monterosso. Reference the park's website if you haven't already?
https://www.parconazionale5terre.it/Eindex.php
You can get around the Corniglia> Manarola section of the Blue but alternate routes will be longer and more strenuous. You could consider taking a bus up to Volastra and hiking down to Manarola. You can do it the other way too but it's reported to be really steep so....
Trail map and difficulty ratings; a black line means a closed trail:
https://www.parconazionale5terre.it/Esentieri-outdoor.php
Info on the Via Dell'Amore:
https://www.parconazionale5terre.it/Eiti_dettaglio.php?id_iti=3575
I've not done this hike myself but have seen the trail between Levanto and Monterosso recommended by others on the forum. It's supposed to be less crowded than the "Blue" and offer some lovely views; no Cinque Terre card needed.
Ferries: Corniglia doesn't have a harbor but you can catch a ferry in any of the other 4. you might want to catch one in Monterosso and take it all the the way to Riomaggiore, or the other way around. Ferries run seasonally; when is your trip?
Schedules and prices here; no need to purchase tickets in advance:
https://www.navigazionegolfodeipoeti.it/en/cinque-terre
Speaking of Corniglia, its train station is located far below the village, requiring catching a little bus that runs between them (€2.50 each way or covered by either of the CT cards) or puffing up the 382-step "Lardarina" stairway.
Swimming: Lots of places to jump in the water but bring water shoes: some are pretty rocky. Here's a thread from last year on the subject:
https://community.ricksteves.com/travel-forum/italy/swimming-in-cinque-terra
