I know 大学毕业 is a verb phrase that means "graduate from university". I
have 2 questions.
(1) In expressing the duration of completed action, which is correct:
他已经毕业了两年大学 or 他已经大学毕业了两年?
Both order are not clear for me, as "了" is not in right position
(2) If I change the word order, is it still grammatically correct:
This order is the most natural one.
“他已经大学毕业两年了” also works. However in daily life it is a tiny little different from “他大学毕业已经两年了”。The reason is “已经” is a kind of emphasize. “他已经大学毕业两年了” sounds like someone is want to know if he is still in college or not, and the respond is "yes he is", two years is additional information. “他大学毕业已经两年了” sounds like, we all know that he has graduated from college, but the period length since that is something strange or important. It can be in the context like “他大学毕业已经两年了，还没找到工作” It has been two years since his graduation from college, but he has not found a job yet.
Sorry I am not a teacher, but a native speaker. I can just tell you what feels natural to me. Wish it helps.