Transition to scheduling with Zoom from another service... CONFUSED

[jamtpg23]

I have taught online with Zoom for years. My students pay me through Square invoices, so I have used the Square Appointments product for years to handle private lesson scheduling. Because of certain limitations and bugs, I plan to move away from that solution and would like to use the Zoom calendar and scheduler moving forward. I have read the documentation, and I have tried a few experiments, but I'm having some trouble accomplishing what I intend. Some clarity, please and thanks very much!

1) With Square Appointments, I set up a weekly recurring lesson time for each student myself at the beginning of each school year. Students are able to log in and cancel/reschedule single appointments as needed throughout the year, but they can't edit their recurring appointment. How do I replicate this workflow with Zoom? Is it Calendar, or Scheduler, or both? I can see that, with Scheduler, someone can find an opening and book it, but how would a student or their parent see, for instance, the lesson they have coming up later in the week in a calendar or list view somewhere, and either cancel it or reschedule it themselves?

2) Currently, new/prospective students can log in and choose an opening for their "consultation" without a recurring appointment for them in the calendar yet. I believe this would be accomplished with Zoom Scheduler, yes?

3) I already connected my Google calendar to Zoom Scheduler. Now I am confused, because when trying to use the calendar in the Zoom desktop app, it's still asking me to connect a calendar. I thought I did that already? Or is connecting a Google calendar to Zoom Scheduler a different thing than connecting a Google calendar to Zoom Calendar? I think I am confused about the intersection of these two products.

If these three questions belong in separate threads, I'll split them up. Thanks in advance!