Actually, most members recommend skipping a day of feeding for digestive health, so yes, your betta will be perfectly fine. If you ever need to leave your betta for longer such as a week, then you can just let them go for the week without food. You would have to take into consideration whether or not the water would be fine for that long though.
Yes, many bettas do just fine eating 6 days a week. I fast mine a day after feeding them frozen bloodworms. My CT got so bloated once I didn't feed him for 2 1/2 days after the worms. Some bettas can go days without food, though it's not recommended to break their eating schedule too much. A weekend will be fine but ideally you will want someone to feed them one of those days.