Is "空时间" a valid phrase in chinese? If not, why not? For example, "你有没有空时间呢"?
In my intuition, 空时间 is most likely a physics terminology (though it isn't).
你有没有空时间呢 doesn't sound right. Try these variants:

你有没有空?
你有没有时间?
你有没有空闲的时间？
你有没有空闲的时候?