free_nirvana
 i am not an investment expert or anyhing close but just want to share my experience with u.
yes, as an f-1 u can buy mutual funds. I have done it. some funds will charge u certain amount up front when u buy them and some will charge u when u sell out yr investment after certain years. First reserch hard to find the kind of fund u like to invest and call them to send u detail information regarding the fund. They will send it to u. Go over that carefully. There will be plenty of things u would not understand...google it... try to understand...call them and ask....or visit a local financial advisor and discuss abt it...just to be clear on opportunity and risks of ur potential investment....
while doing so, don't chase the investment returns of past years...past performance does not gurantee future performance....never forget that......and remember, u have to own them for certain time before u can sell them.
there are lot of differnet kind of products(mutual funds) particular brand(like vanguard, fidelity etc.) sells. For example, small caps, large caps, mid caps, chinese stocks, indian or any country, emerging markets, europes, gold and commodities related.....whole lot of.....
I had bought a china related mutual fund few years back and luckily sold it long before 08 market crash. I had done couple of month of research.....my entry and exit from the fund was luckiyl right. That was my first exposure too. so do proper research.

I am not an expert but my take on market for now is : it is still pricey....u can find yr long term investment in cheaper rates may be by the end of summer....so if i were u, i would wait and research.....however gloomy japan looks now, i think, longer term prospect of japanese market is brighter than most of G-7 economies....I would not go to emerging markets right now unless u can find real gems......
but what i know??? do yr proper research. Good Luck.