Cotton twill for the coat. You might also use something nicer like cotton velvet or velveteen (not the stretch kind or the thick kind). This time of year, you should have no problems finding fake fur trim for the coat. Wal-Mart even sells it - the stuff is marketed as "Santa Claus" costume trim.
To be honest, the fur looks like sheep's wool - raw and unprocessed. Since you probably don't want to mess with that (lots of reasons why you might not want to), try printing a picture out and taking it with you to the fabric store. Show it to the ladies and see if they can point you to something. I would suggest not using the maribou boas, though. It's not very feathery.
For the Chinese-style shirt, it looks like it's white with a light blue lining and an ocean blue bias tape trim. That makes it easier, I think! You would probably be able to cut out the same size pieces of your white material (use a cotton that's thick enough that you can't see through it) and light blue material (you can use a "lining" material) wrong sides together...then bind the edges together with ocean blue bias tape.
EDIT: Oh, I have a Chinese-style pattern at home that would probably be good for the shirt!
The general shape seems very similar in one of the views on the shirt.
BTW, who is the lovely lady in black in the third picture, lower left?? That outfit looks pretty cool from what I can tell. CLAMP always have such nice character designs...
Ooh, looky! Kyo wa...Mokona! Puu-puu~! ^_^