answer all the questions

In question 1 part (a) you have a standard utility maximisation problem, which is solved in the usual way (i.e., as you learned in ECON601).
In part (c) you have another standard utility maximisation problem -- choosing food and water consumption to maximise a utility function given a budget constraint -- but now your "income" depends on your neighbour's water consumption: see the RHS of the budget equation (**).  Therefore, when you apply the usual method to solve for the optimal consumption of food and water, your answers will be functions of your neighbour's water consumption.
You should also note from (**) that you only pay $(p2/2) per unit of water in part (c), so that is the "price" of water from your perspective.