So the pump has been running for about 4 hours and I turned it off so I could sleep at night without the noise but I just want to make sure that my betta will be OK. I've heard that it's bad and I've also heard that they can survive without it. But I'd turn the pump back on In the morning anyway when I woke up. I just want to make sure.

Yes fine.

Yes bettas will do just fine without an air pump. I'd just turn it off and leave it off as that will provide better stability than turning it off and on every day.