The vitamin E will settle out/float in the water, she won't get enough. You can just put the capsule in her beak and push it back, she'll swallow it.
If I have to keep a bird warm, I bring them into my spare bathroom at night, in a crate, or I put them in my shower with doors, with towels on the floor of it. There is room in there for a dish of food and water, and then I can sleep with no worries, they'll be warm and can't go anywhere. Clean up is usually no big deal, the towels go in the wash. You could also use puppy pads if you have them, and just toss them.
If I have to keep a bird warm, I bring them into my spare bathroom at night, in a crate, or I put them in my shower with doors, with towels on the floor of it. There is room in there for a dish of food and water, and then I can sleep with no worries, they'll be warm and can't go anywhere. Clean up is usually no big deal, the towels go in the wash. You could also use puppy pads if you have them, and just toss them.