When your interceptors are patrolling a target (have it in their purple circle) which is direct attacked by enemy bombers, those bombers will take big damage.
When your enemy is patrolling with a stack with less interceptors (inc. tech) than yours and your circles overlap, you'll eventually win or force him to withdraw. Keep in mind that there's the "first hit" thing in play: the player who first patrols an area ticks first and can move away before the second player even has a chance to tick. Attack damage is bigger than defense damage for fighters.
Leaving planes over the battlefield overnight is always a huge risk; only do it when you're SURE you have superiority, otherwise find a safe place. Also, be sure that the enemy can't move a big AA stack underneath them when you're sleeping. Generally, better safe than sorry, move them to a safe patrol place before going to sleep (yes, even if that means you may lose ground troops because they weren't protected).
Don't attack enemy airbases with fighters; there's strats for that.
