As you know, in negative sentences, "了" is not used with "没有". So you cannot say "我大学还没有毕业了". Instead, you should say "我大学还没有毕业".
However, "你大学毕业了没有" is NOT a negative sentence, but a question, which is equal to "你大学毕业了吗".
Here are some other examples:
你吃饭了没有? = 你吃饭了吗?
你结婚了没有? = 你结婚了吗?
It should be noted that if you need to use "不" rather than "没有" to answer a question, this question must not end with "没有".
e.g.
你明天来吗? You cannot say "你明天来没有?", which is grammatically incorrect.
"Lastly, why does the main noun, 大学, appear after the verb, 毕业?"
I think you meant to say "Lastly, why does the main noun, 大学, appear BEFORE the verb, 毕业?"
There is no special reason for it. We always say "大学/中学/小学毕业" instead of "毕业大学/中学/小学".