All Royal Caribbean and Celebrity ships have towels available in the pool areas to be returned after use to a container in the same area, so no problem.
Yes, towels are provide for pool and shore excursions.
You will have plain white towels for in cabin use and also coloured towels for the pool area. There will also be a polite notice stating if you do not return pool towels to cabin there will be a $20 charge. You can also obtain extra towels from around the pool and you have to sign them in and out with your seapass card.
As before towels are provided,however the room towels are bath towels not bath sheets,therefore if you are anything above a size 16 they will not go round you.No larger towels available,but our steward brought us bath robes to use during our cruise.