Asians do need to score higher on the SAT than whites and others. Before the SAT changed from the 1600 point to 2400 point scale, there was a study that admitted Asians scored 50 points higher than whites. (I have read that Asians need to score 140 points more than whites today on the 2400 scale - maybe things have become more difficult for Asians.)

Look under Bias against Asians and whites - note that the guy Thomas Espenshade is a Princeton professor.

Many of the US elite colleges have very large endowments and offer great aid to those admitted. While some schools take need into consideration during admissions, there are many top schools that do not (not for US citizens anyway; story can be different for internationals).