Plants require oxygen, as their cells break down glucose by the process of respiration, just as ours do. However plants produce their own oxygen as a byproduct of photosynthesis, so they are self-sustaining in this regard. Plants also do not need food, since they make that by photosynthesis as well; they do need water, as well as access to light energy.
There are quite a number of organisms that do not require oxygen to live. Obligate anaerobes are microorganisms that require an oxygen-free environment. Earth species of anaerobes have been studied carefully, with the idea that life on other planets could have metabolisms that are similar.
At this point no living organism has been identified that can exist without water. There are some microorganisms that can survive being completely dried out, but they become inactive, and do require water to carry on their life processes.