You were close with the first one! You have to remember that when you use 'the' with plural things it becomes na - Tá uisce ag na madraí.
And I believe you overthought the other two! All you have to do to get from "'the dog has water' to 'does the dog have water' is chafe tá to an bhfuil
So an bhfuil uisce ag an madra. Try again with 'do the dogs have water'
From my understanding, the 'ag' on its own is just 'at', which is used in the sense of having in English. The modifiers (agam, agat, aige, aici, etc.) serve as 'at me' (in the sense of 'I have') or 'at you' (in the sense of 'you have'). When you are using a subject other than a pronoun, however, you'll use only the basic 'ag' plus the noun form, which will, in certain circumstances, have an eclipsis as the 'object' of the preposition (even though they become the subject in English). In this case, though, 'iasc' doesn't actually have an eclipsis.