How to ask for approval letter from dean? I've studied in this college for Diploma and have now proceeded to the Bachelor's Degree. I am facing some problem that may cause me to extend my course.

The system of the faculty is like this: When you want to take certain subject, you need to pass all the prerequisite subject for that subject in the previous semester. This is reasonable by far. The prerequisite subjects are listed on the booklet sent to us during the faculty briefing.

But up until recently (my second last semester), I was told by the faculty staff that I cannot take my FYP (Final Year Project) because I did not finish all my prerequisite subjects. I was shocked and I showed her that the booklet of faculty briefing didn't state that at anywhere. She told me that this information is stated on a separate website specially for FYP. The problem is, I didn't have a single clue about the website before I went to take it. How was I suppose to know this information in the past semester?

There is no post about this information in the college official bulletin board website, and I didn't even receive a single email about this. The staff told me that I should be alert with all that kind of information.

I tried to appeal to the dean, wanted to talk about my issue face to face. But the staff stopped me and didn't allow me to talk with the dean. The reason they give is that dean has no time for me. They suggested me to write a formal letter and wait for dean's reply.

I have submitted my formal letter, but the due date for the registration of FYP is few days later. If they do not reply me for this issue, I cannot take my FYP in this semester. If this happen, I will have to wait another year just to take the single subject for two semesters (FYP part 1 and 2), and my graduation will have to delayed for one whole year. I don't want to extend my course because of this reason.

They do have a course structure for us to follow, but it didn't force us to take exactly same as the course structure, so we can plan our course before every semester. I didn't follow it because I need to handle harder subject in the earlier semester so that I can focus on my FYP in the later semester.

What should I do and try, so that I will not have to extend my course? I have also tried emailing to the dean about this problem.
I don't know anything about your university or its normal practices, so this is only tentative. 

If your university has any sort of office for student advocacy, go to them with your concerns. Hidden rules aren't appropriate in any situation, though they may be permitted - unfortunately. 

In case there is no such office, go to any professor that you trust and who knows you well, and ask him/her to be your advocate. The dean will certainly offer a bit of time to a professor that they won't to you. You are asking for an exception to the "rules". Make sure that you have a basis for the exception (you have the needed knowledge to proceed) and not just that the rule is unfair if it is hidden. 

Unfortunately, you are possibly making people uncomfortable and when that happens they sometimes behave badly. The more confrontational you make it, the worse it may get, so be aware of the risks.