First of, I would not reveal the dollar amount to invest. There is no such thing as too much or two little. But for margin account, I believe, it requires two grands in minimum fund.

To learn about investing, take a primer course in Fundamentals of Investing at a local community college, check out investing materials from local library, read business/financial journals etc whichever makes sense to you. I think textbooks still provide the most comprehensive coverage of concepts and illustrations to get a good feel of what it's all about.

To start trading, you can google yourself all the way to your first trade but background with bare minimum knowledge of investing would definitely serve in your favor. Coz no matter whether you are trading or investing, both fundamental vs technical analysis come into picture. Google them if you are unfamiliar with these concepts.

For the amount of fund you have mentioned, I guess it's okay to invest using an online brokerage. Among them, Trade King and Ameritrade were pretty well received by one of Kiplinger's or Money magazine issues this year.

F1 visa holder owning Real estate?
Anyone can own property in US remember the Japanese owned the "Rockafela" Center in NY a few decades ago. Getting back to residential real estate and speaking from second hand experience, the brother of a college mate owned a house while both were on F1.