There are quite a few cutscenes and events that lead up to Fangmei's birthday. This is a huge secret and quite hard to do. Here's how in many steps.
Firstly on disc 2 find Aillin in pigeon park. There should be a cutscene where Ryo watches her practice martial arts. Then, when you have that job airing out books at Man Mo Temple, make sure you get the cutscene in which fangmei brings you tea. This might only occur if you are fast at moving the books, and i think it occurs the day after you have to catch the leaves.
Next when doing the chawan sign, teacups, you will have a fight in Man Mo park. You need to LOSE this fight to get a cutscene and make sure you dont miss out on the other events.
After the chawan signs, and before finding Ren, go to the backyard of the Man Mo Temple before 3pm. If it is a sunny day another scene will trigger, followed by another at Man Mo Restaurant.
Between 28th February and 3rd March, you should find Aillin in an antique shop in the wisemen quarter. She will tell you about Fangmei's birthday on the 3rd of March.
Find Fangmei and follow her into a Tailer Shop. Then you should be able to buy her a present for HK$150.
On the 3rd of march, go into Xiuying's room to trigger an event. The following day another event should happen.
To make this work, you have to talk to Fangmei a lot throughout the disc until she calls you Ryo instead of Hazuki.
This is a lenthy series of side quests that can happen involving many different side games and culminate in you getting 3 medals. You can do this on disc 2.
Firstly on disc 2, find aillin in pigeon park. There should be cutscene where Ryo watches her practice martial arts. Then go to the tomato mart in golden quarter and talk to Izumi at the desk.
Near the come over guest house, there is a pawnshop which has a little alley beside it, go through the alley and there is a door which is open (after this and on disc 1 this is boarded up). Go through the door and you will go to a new area. On the table you will find a bronze medal and loads of free capsule toys.
Once you have the bronze medal, you now have access to the third floor of the arcade, which was previously out of bounds.
You can play HK$20 to watch a fighting match or compete. The first match is against Aillin. If you beat you can return and pay again to fight Izumi (This includes a QTE and is a wierd and very tough fight!). If you beat her you get the silver medal.
Go to the tomato mart and press X. You will enter the Duck race, you have to win first place. Once you have won the duck race, go to the backyard of Man Mo temple. You will have to go to the catching leaves tree and have to catch 2 or more leaves at the same time. If you do this you will see a white feather. You have to catch the white feather to win a duck.
Once you have the duck, go back to the tomato mart and enter the duck race. Win it and have the Gold Medal!
Like the first Shenmue game, the second installment also contains a bad ending if you delay too long. It happens on July 31st. Once you go to sleep on that night, you will get the cutscene. The easiest way to get it is when you are searching for the 4 Wude there is a QTE in a barbershop. If you fail it (by pressing A) then you are given the opportunity to wait a day. If you keep doing this one day should past in approximately 2 minutes. If you dont want to do it yourself here's a short explanation of what happens. Against a black background, Ryo takes out the phoenix mirror, there is a large red light, and the red centre of the mirror turns black. Lan Di appears along with a white flash and Ryo calling out in Pain. The scene then changes to Shenhua on a cliff in guillin. She says "The dragon calls the dark clouds and hides the morning star....the path is closed and the hope of meeting is lost" and then Lan-DI appears. He says "i shall take your power for the Chiyoumen" and then the Game over screen appears.
There are many cool rooms hidden away in this building. Here is a rundown of some of them:
12th Floor: Dural room.
3rd Floor: Convent/Church.
6th Floor: Karate School.
1st Floor: Two shops, opposite knife stalls, selling move scrolls.