Let's take the idea of practical magic and run with it, shall we? A quick glance into Thermodynamics allows us to see that there is no such thing as "cold", just lack of heat. Elsa (and Frozone, and Iceman, etc) can NOT actually "project" ice and cold. Instead, she has a magical ability to selectively absorb energy from her environment. Control over this energy absorption can lead her to be able to create ice sculptures as long as there is water in the air to condense. Remember when she took her gloves off and held the metal objects for the Queen ceremony? Water immediately began condensing and freezing on the metal surface, because metal is a good conductor. It stands to reason someone who has this ability would likely have conductive objects have energy drawn from them faster, especially via contact.
I'm building up to the following answer: Elsa can, in fact, rely upon her magic to not need to worry about solid waste removal, water collection, and food preparation. She is taking the energy out of the environment, and it's gotta go somewhere. Likely she is absorbing it directly in to herself (she was locked in a room with no visitors for many years since her parents croaked, the guards were not allowed to visit). She is, in essence, "eating" the energy she requires right out of the environment itself, so it stands to reason that she wouldn't get hungry. And, if she is not consuming solid foods in any way, there's no reason for her to need a system for solid waste removal. Her water intake can be explained by water in the air directly condensing in her lungs (also, she can condense large quantities of water right out of the air, so more if necessary is available on demand), at a rate which can be absorbed into her blood stream, leaving only the issue of liquid waste removal. Due to her unique metabolic situation (she absorbs energy from her environment) there is likely less waste and more efficiency. But as an engineer, I'm not going to handwave this away with magic, because Thermodynamics might explain the reason for everything else, but Thermo also says the scant waste has to go SOMEWHERE. So, Ice Chamber Pot for peeing, and that's it.