N300 C3000 Will the C3000 reset itself after a power outage? I am away from home several days often

theoretically it should. I've had mine reboot normally after power failures. 

But if you're getting that many power failures, I'd look into a backup power supply. they're fairly inexpensive and are great to protect expensive electronics. After loosing 1 router, I invested in a backup power supply. nothing like loosing a several hundred dollar router to make a backup power supply look cheap.