- How should I ask for an internship or research assistant position?
This initiative is laudable, but misplaced. It is useless to send unsolicited emails to high-end research faculty all over the globe. (I get about 100 of these per year, many from India or China.) These faculty are usually very busy and are themselves overrun by (often free) assistance requests from students at their own university. If you really want to do this, go to a local university. Impress the faculty with your preparation and grades. (For economics, this is usually good knowledge and grades in programming, statistics, and intro economics.)
- Should I major in finance or business in my undergraduate studies?
It's not bad, but not necessary, either. Majoring in economics, statistics, computer science, or math is equally good preparation.