No; of course babies in nappies are not allowed in the pool - how unhygenic. No; there is no baby food or nappies on board - you have to bring them with you. Yes; there is a toddlers club but you have to stay there with the babies to interact with them. No; the babysitting will not look after the 10m old. All this info is on the RCL websit.
We cruised on the Navigator of the Seas last year did not have a baby with us but saw a few on board - Fantastic ship loads of facilities for all age groups - Staff extremely helpful - 10mth old will probably eat semi solid food the casual dinning areas of windjammer and jade have a massive selection of food and would say that there should be a decent selection that would be easy to mash down again the staff are v helpful would suggest that if you feed your little one jar food etc that you take some with you I have seen bottles being warmed etc but need to take own formula and make same as you would in any hotel . Nappies cant remember if they sell any onboard so I would take what you need but doing the med you will have access to shops,chemists etc- There is plenty of different areas on board for all ages and you and your family should have a great time.