Yes they do freshly roast chicken and it's cheap say around 3 quid for a whole one. Don't forget your AI hotel will also do chicken too! Walmart will take dollars or pesos (but dont take $100 USD notes). They give a great rate for dollars so if you have them use them there, but pesos I think will be better for you overall.
Oh and water, the hotel will be more than happy to let you fill up your water bottles with purified water no charge. If that is not enough you might want to think about buying a "garrafon" these are 20 litre bottles that cost just over a quid downtown, probably in the hotel zone you might have to pay 2 quid You should be able to buy them from the convenience stores. Staying at Dos Playas you are right next to a store called OXXO which should have them.