Can your fingernail scratch the iPhone 6 screen?

If you have diamonds glued to your nails or you have adamantine claws that pop out of your fingers, certainly. 😉

Just as it would be almost impossible to scratch a car window with your fingernails, you can't scratch the screen with your fingernails.

For what it's worth, so far, my kitten hasn't been able to scratch the screen, either. Try as I might, I have trouble keeping her away from the phone.

The screen is made of some sort of hardened glass. I don't recall that Apple has ever said specifically what kind though I've heard that its some version of Gorilla Glass. Scratching the phone with your fingernails, even around the edges shouldn't be a problem. However, dropping it while you're asleep could. Perhaps you should consider putting it in a protective case? If only at night.

Probably not but, in your special situation, I'd definitely have a case and a screen protector on the phone.