No, this is not just a normal thing you should get used to. Your post actually makes me wonder if this is a prank post, it sounds that absurd!
Yes, this person is clearly going through something. Most of us have been there, but hopefully not in a stranger's house. You need to set some boundaries. If you can do this in a calm, compassionate way, that would be ideal. Try and see this lady with kindness and assume she means you no harm when you talk to her. Think about the way you talk to children, people who are ill, or people in mourning if you have experience with those. Ideally, keep your tone caring, even if you're confused and angry about all this stuff. Tell her you have a few requests and the completely logical reasons why you need to keep the fridge plugged in, etc. Figure out what is ok for you and what is not- are you ok with the blankets, but not the unplugging? Do you want absolutely all of it to stop? Ask her clearly if the reason she unplugged the fridge is because it's too loud for her, and whatever other things you decide are not acceptable to you and tell her you're sorry but we really have to leave it plugged in so the food doesn't spoil. This sounds like a person battling for their sanity and you can try to be supportive if you have that in you. Decide for yourself if you're ok with her using your room for her mental health retreat. It sounds like you're not. It would probably be better for both of you for her to be in a place she can cry and make messes to her heart's content without you or your husband passing judgement on her behavior.
It also sounds like you do not have very good communication with her. Are you able to simply talk to each other? Does she comprehend things when you talk? Does she talk like a reasonable person? Remaining in mutual awkward silence helps no one.
Your other option is to let her know that your space is not just compatible with their needs and they will need to find another place within a reasonable amount of time- you would be within your rights technically to ask her to leave immediately, but you might want to talk to her and find out what the situation is and whether she can find another place to go within, say 24 hours. You can bring up the noise being non-negotiable or the windows being unsuitable for her, really. A hotel or weekly motel might be a much better option. She might act angry about it, but try not to get upset yourself. She will probably calm down if you leave her alone for a while. You can tell her it's nothing personal, you're sure she's a good person but it's just not a good fit for her needs. You can even help her pick out a motel if you can do it in a kind way, assuming your place isn't on a remote mountaintop or something.
She might end up leaving you a bad review no matter what path you choose, but you have an excellent case to get it removed, or you could just start a new account using a different email when you want to continue since you've had so few guests. Definitely don't get involved in a bad review war with her. There's nothing to be gained from fighting with people online, especially when they're going through a breakdown. And remember, only there by the grace of god go the rest of us "stable" people!