OK here's some background. I'm from a Southeast Asian country and right now I'm studying in a Japanese university. She's a Japanese and she's been to my country to study and she can also speak my language well (I speak Japanese well also).
Off topic, but that's really sweet dude, I've always wanted to do some sort of study abroad program! It's also very cool that you're multilingual.
We started to know each other by hanging out with other friends, but I tried asking her to hang out just the two of us, and since then we've hang out just the two of us several times.
One of the first things people will tell you on this website is that if you like a girl and want to be more than just her friend, never use friendship as a bridge to get there. And... they're right. That is a bad strategy and tends not to work well unless the girl has a very high interest in you... and even then, as you will learn, it sets the stage for a less than ideal dynamic in your interactions with her.
And very good. You recognized intuitively that you were not going to get where you wanted to be if you didn't isolate the girl. And you did. That was a good move.
I've even been to her room, and vice versa, well mainly to study together heh.
When you want quality advice from people, there is no room for innuendo and assumption. Is all you did study together, or did you *wink wink* study together (and you'll have to explain what the *wink wink* means).
I think we clicked together personality wise, we always have lots of laugh when we are together, have many common interest, etc.
Good. Depending on your intentions, that "click" is more important than your commonalities. I don't know how long you've known this girl, but it doesn't sound like you have known her well enough to be legitimately informed enough to seriously consider her as relationship material. That being said, it sounds like from what you're describing that you had some sort of connection going on.
around 2 weeks after we started hanging out together I asked whether she would be my girlfriend, but she said that she only viewed me as a friend (ack, friendzone), but said that she would be really happy if we can still continue hanging out together again.
Yes. The dreaded friendzone. There are a few things to gleam from this. First, do not ask a girl to be your girlfriend. Read The Book of Pook, located at the bottom of the page under the link "DJ Bible". You are "The Great Catch", and as The Great Catch, why would you ever propose that someone put you in a cage (IE, a relationship)? It is much better to be a good man and wait for the girl to bring up the topic of exclusivity. What you're doing by asking her to be your girlfriend is telegraphing interest to the point that you want to take her vagina off of the sexual market place. That says quite a bit there my friend.
The reasons why this happened could be numerous, but it probably ultimately distills down to one thing: When you think back to how you acted and how you described how you acted, did you act like a friend or a boyfriend? To quote Pook, "A friend you'll be, a friend she'll see". It does not sound like you were a sexual threat to her... now be mindful that when I say this, I'm not insinuating that you need to be the sort of man who is actually physically or illegally threatening. What I mean is that you have to have a defined sexual presence about you that differentiates you from all the dudes out there that just want to be her friend. You can't be afraid to touch her, you can't be afraid to lead her, guide her, put your arm around her, kiss her, ect. In short, you should not be fearful, ashamed, or anything but embraceful of your desires as a man and masculinity. To quote Pook again, "Only the sexual ones get the girls".
So fast forward, another 2 weeks passed, and we'll meet again and have dinner since I last met her. I still don't wanna give up her.
You really should though pal. It's very difficult to salvage these situations and almost never worth the time it takes. And when you think about it, would you really want to have to invest so heavily in a girl who doesn't see enough in you to want to be your girlfriend? Find a more useful perspective to see this from. You have most likely elevated this girl to a higher status than yourself, which is called pedestalling her.... putting her on a pedestal. And that is one of the most dangerous things a man can do.
My question is:
* Should I ask her to hang out on valentine's day, to show her that I really think that much of her?
No. What you need to do is take some time to study the ins and outs of attraction and once you've done that, ask yourself if this will be an action that will increase or decrease attraction. Chasing girls is never a good idea, ever. It will only decrease attraction. This will not do anything for you except continue to give you an outlet to spend your money. And would you really want a girl that is such a prima donna that it is necessary for you to make such grandiose gestures to secure her attention? I hope not.
* Should I go out with other girl on valentine's day, to show her that I'm not needy? (PS: I have many other close girl friends, and it wouldn't be difficult for me to get one of them to go out with me on valentine)
You should go out with another girl on Valentines day, but not to show her you aren't needy, but to demonstrate that to yourself and because you want to. Turning action in to a mechanism for revenge may be successful in the short term, but it's more than likely not going to bring you where you want to be. And a real man doesn't need to do stuff like that because he just doesn't have the time... he's too busy being a man, after all 
Go out with as many women as you can right now!
* Should I just spend valentine's day other ways, like for example playing with many friends together? (which perhaps might include her)
Do whatever you want to for valentines day. You don't have to take out a girl. Do what YOU want. I would just make sure that whatever you do, you do not include the girl of which you speak for all of the reasons I have said.
Thanks for the advice!
