Here are some questions about this, and my answers.

Q: How would she eat?

A: I don't think Elsa eats ice and snow for breakfast, lunch, and dinner. So the only near wildlife were those man-eating wolves from the sled scene with Anna and Kristoff. Of course she could go hunting. Unfortunately, Elsa doesn't know a thing about hunting. Therefore, I have kindly provided the picture above to visually display what would certainly happen if she attempted this (don't worry, it's not real. Hopefully.) Otherwise, she would starve to death. 

Q: Bathroom situation?

A: Just go in the snow. Honestly, there's no one else in the mountains. There probably would be a pool of yellow snow that would increasingly get larger by the day (and monthly be replaced with red snow if you get what I mean) Now, she is a queen. So she'll probably want to have standards. I'm not saying that making an ice toilet with ice pipes is possible, but that's the best I could think of.

Q: Sanity?

A: She's been locked in a room since she was a little girl. Elsa lost her sanity a long time ago, but Disney ain't making her go crazy. If you seen that Frozen Fever, she seems to have got a little tipsy. Maybe she was drunk. Who knows? Who cares?

Q: What about Anna, Hans, and all that?

Hans would have become king, stabbed Kristoff. Sven would turn into a llama while Olaf will be in unity with the element of water. Anna would be in an abusive relationship, or would also be stabbed. Soon Hans would ally with Donald Trump and try to take over the world, but would ultimately be beaten by whatever good that is left in the world.

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I might make a part 2 for this...