Apple Care doesn’t cover liquid damage. Apple Care+ does. If you do consider it go for Apple Care+. I am glad I got it when I got my Macbook Pro. 8 months later accidental liquid damage at work. With Apple Care+ cost me 299$ without it 1700$. Everything got replaced and from start to finish the entire process took 48 hours. You never know what can happen no matter how careful you are. Is not always your fault. Accidents happen.

I doubt that you can use it with Apple TV. Only iPhone has features that works with Apple TV