Yes! Just start Early and leave it open before you go to sleep.
You can safely lock your iPhone or you can start the Night Mode.

Just swipe from the left or the right edge of the main screen, or tap on the icon with a moon.
While in the Night Mode, you can swipe up or down anywhere on the screen to adjust brightness.
Swiping left or right will close the Night Mode.

If you are using the Night Mode, the screen will be on overnight. That will consume a lot of battery power. That is why it is highly recommended to leave your iPhone plugged.
If charging is not an option, just start Early and lock your phone. This will preserve battery power.

Yes, but you need to check theese two things:
1. Go to iPhone Settings and then to Notifications and make sure that notifications are allowed for Early.
2. Make sure that your iPhone is not in Do Not Disturb or Silent mode.

Just swipe it to the right or to the left.
To re-enable it, just swipe again.

They show you how many days in a row you won a game against the alarm. You need to win at least once a day to keep the streak going.