Hm, I've always read that bettas prefer soft, acidic water and have had success breeding them under such conditions. Of course, they're highly adaptable, so I'm sure hard water wouldn't be out of the question. Curious to see what others say.
As for the crayfish, I agree that it's not a smart idea. While it may not be the source of the stress, it's definitely a danger to your betta, especially when it gets older. He'll begin to try and grab fish out of the water as he gets larger (and boy, will he get big) and eventually be successful. They're not as slow as they look and they can extend those claws with breakneck speed. Just a heads up!
Bettafish15, I believe the water is cloudy because it's cycling. I don't think it needs water changes yet. I could be mistaken, but that's my impression from the photos.