Thank you, I almost forgot about this post...
If it's one of the Oasis or Quantum class ships, your teens will probably love it.
Yes - the cruise planner will show the discounts, most often it was beverage package, internet, and some excursions yes. Spa, specialty dining packages.. etc
Now, as far as when they start I'm not 100% sure as we booked fairly last minute.
They kept popping up here and there, we got emails notifying us sometimes - but best if you follow the Royal carribean cruise blog, he not only has a lot of general info, also lets everyone know if there is a new sale in the cruise planner.
If you book something and a better sale pops up later, you can cancel and rebook - up to 3 days before sailing ( I believe)
I'm sure you will love your Royal cruise, but if time and $ permits, definitely try Disney at least once
Oh and
to DIS
There is also a Royal forum here