No it says the have bathrooms, the fact they don't use them suggests they don't. You stated that because people drank ale etc. in the game and water was not sold it meant people did not drink water due to bacteria within it (or something along those lines) which is a preposterous statement. To say people don't use bathrooms on Nirn simply because they don't in the game (for obvious reasons) is also preposterous. Children obviously must drink milk and water on Nirn, they might not in the game, but they still do if you understand me.
1. The evidence of bathroom facilities implies they use bathrooms. Unless - (like birds) - everyone on Nirn has one single orifice for passing waste it's reasonable to assume that they have - like us - an anus for solids, and a urethra for liquids.
2. It's very likely that people would not drink water because it would make them sick. They would drink mead and ale because it did not make them sick. This is implied in the game world with a reasonable degree of clarity.
3. One of your statements appears to contradict another of your statements re bathrooms.
4. Whilst undoubtedly children up to a certain age were svckled at the teat, they is no evidence to suggest that they would have been given water. - (in fact it is a fact that IRL children were also given beer to drink rather than water).
What you have to realise is that social mores regarding beer were not the same in earlier and indeed are not the same in many cultures in the present time.