Ferry Cinque Terre

Yes, there is a day pass. Of course you can't visit Corniglia directly from the ferry since it is located away from the sea.

Yes. Easy to buy before you board at the ticket booth at each of the towns the ferry serves. The ferry also goes to some non-CT towns such as Levanto and Porto Venere. Enjoy!

We spent 1 night in La Spezia to scout out the ferry departure location/schedule and secure our suitcases with the hotel while we hiked the Cinque Terre.
Early the next morning, we walked to the ferry, purchased 1 way tix to the last stop. Hiked with light backpacks with 1 change of socks and underwear, toothbrush, and stayed in Vernazza 1 night. Finished the hike the next day and took the train back to La Spezia. Wonderful experience. Rain can cause trail closures. Must have reservations which are timed.

One of our favorite places in Italy with great food, local culture, NO cars, spectacular scenery. Early morning and late afternoon/evening are magical as most crowds/tours have disappeared. We visited late May/early June.

Must have reservations which are timed.

It sounds like the OP is only interested traveling by ferry but if hiking, the only trail section you need timed reservations for is the Via del Amore (on the Sentiero Azzurro.)

https://www.parconazionale5terre.it/Eiti_dettaglio.php?id_iti=3575
https://www.cinqueterre.eu.com/en/cinque-terre-via-dell-amore

During certain very busy times of the year or special events, there may be enforced one-way trekking hours on the Sentiero Azzurro, which also requires a Treno or Trekking card to access.

Info on ferry schedules and passes:
https://www.cinqueterre.eu.com/en/boat-excursions

The ferries aren't necessarily the most efficient method to get from place-to-place as it takes awhile to dock, load and unload the boats. I'd have a Plan B in case of a rainy day: not the most fun place to sightsee when wet/stormy.