Plaza Gardens is used basically as an overflow breakfast when the hotels are busy. To have breakfast at the Plaza you ask at check in, the same way you would for a normal breakfast voucher. If they are using the Plaza during your visit, you will be given a voucher with a timeslot, just the same as you would for the hotel. The Plaza is not always open for breakfast, it might be a different restaurant or they might not have the breakfast in the park option during your visit.
For Disneyland Hotel, you would have to pay, I know the prices went up last year, I think it is around €35 per adult for breakfast. The Disneyland Hotel breakfast is only "free" for those staying at the Disneyland hotel. It is not covered on the breakfast voucher of the other hotels