What happens when user's browser is closed?

I have a couple of pre-sale questions:

Let's say that I have a user previously authorized permission to receive pushcrew notifications from my website. What happens when I push a notification to that user through the REST API when that user's browser is completely closed (not running). Do I get an error? Does the user receive the notification when she launches her browser next time? Something else?
Can pushcrew notifications be scheduled for a specific future time when pushed through the REST API?

Thanks.