No, you must visit a U.S. consulate in the country where you live. You cannot make an appointment for a visa in another country if you are not a citizen of that country.
No, participation in college sports in the USA does not affect player licenses or team registrations in your home country. In most cases, college athletes remain loyal to their home clubs and often participate in competitions or games in their home ...
You can apply for your visa as soon as you receive your I-20, but no earlier than 120 days before your studies begin. This date is listed under Start on Studies on your I-20.