What if a customer enters in a voucher code twice?

Enrolmy will not recognise duplicate voucher codes, you will need to submit the voucher code to the NSW portal in order to get confirmation that it has already been used

Are there examples for why/when/how a voucher credit note would just become unapplied without me triggering this?

No, but you could easily unapply the credit note from the invoice (via Money tab or Xero) without realising it for a voucher

When the Mark as rejected button is ticked, what happens to the invoice?

This will only void the credit note and NOT the invoice. If you don’t want to keep the booking then you can go through the booking cancellation process to inform the customer that the booking has been cancelled

If I want to enter a voucher code manually, would I be able to do this on a draft invoice?

Yes, you will be able to!

If I rebook attendees for next term myself, are the guardians still able to submit their voucher details?

Re-enrolling the attendees yourself will also mean that you will have to take all the voucher detail yourself and apply them against the invoice. 

If you wish to use the voucher feature then it would be best to have the customers make the bookings themselves and submit the voucher details in the process