Answering a couple of my own questions (but still welcome more info):
1) Dates are stored in UTC time. Google found that info for me here: http://www.telerik.com/help/aspnet-ajax/scheduler-working-with-time-values.html
2) There's no recurring tems created in the database, just a recurrence rule that appears to be an offshoot of the iCalendar formats. Any suggestions on ways to handle the need to tie a clock-in to a specific occurence of a recurring appointment?
3) The Appointment class apparently includes a RecurrenceRule object which has an Occurences property that iterates through occurences. Is there a way to access a collection of Appointment class objects on pages that don't have a RadScheduler control so that I could do things like searching for matching appointments in my check-in code? Is there an alternate way of dealing with that sort of issue? Google brought me http://www.telerik.com/help/aspnet-ajax/scheduler-working-with-recurring-appointments.html
but it doesn't seem to cover a non-RadScheduler page.