They are interchangeable, the only difference is that 되다 is more used in colloquial situations.

They're the same. That's why the grammar point always shows up as 아/어/여야 되다/하다. ^^ 되다 would also more likely be used with a verb already ending it 하다 so that it's not 해야 해요. But either could be used. I agree with Hyejeong.

Technically, they are same. But, in my opinion there is a little difference on delivering nuance. 어야 하다. could be more like "need to do." And 어야 되다. is more like "need to be." For example, 일을 하려면 밥을 먹어야 한다. Is more like "you need to eat to perform your work." 일을 하려면 밥을 먹어야 된다. Is more like "you better be eaten to perform your work." But this is just my opinion. And there's no difference in general dictionary.