[X] I should build something! – Alchemy may be able to solve all problems. If stepping on air is possible, breathing under water should not be out of reach. It will take you longer than with any other solution … but the solution will be here to stay. (High DC on preparation time, low DC on time spent under water.)
[X] I'm a wizard. I need a spell. – A charm or a transfiguration? You are not too sure as to how to solve this effectively, but it should be about the same as using a spell … right? (Medium DC on preparation time, medium DC on time spent under water.)
[X] I might need something to drink. – Any effect a plant can do, a potion can do better. That is something that you know for sure. It will take you a while to gather the ingredients and brew the potion, and you first need to spend some time looking for one at all; but it should be possible. (Medium DC on preparation time, medium DC on time spent under water.)
[X] There must be something I can eat … – Honestly, your third-year curriculum doesn't give you too much to work with here. But it should be possible to find a plant that can allow you to spend some time under-water. (Low DC on preparation time, high DC on time spent under water.)