Is it dangerous or unhealthy to sing in a very quiet voice to yourself and sing very high at the same time? 

It's not unhealthy to sing quietly, Demi! In fact, the ability to sing quietly (and high) are both signs of a healthy voice. What we want to avoid is singing with too much airiness or breathy tone. But there's nothing wrong with quiet singing. 

Ohhh I see. Thank you!

Sure thing, Demi!