I woukld love to see the answers to those questions
though I would like to point out to some of those tests you will have biased samples.
For example SAT’s many yeshivas do not allow their talmidim to take SAT’s and others make it difficult (YOu Need the Yeshiva’s help to take it as they are offered on Shabbos unless a dispensation is granted). So for Yeshiva guys in many settigns the only ones who are taking the SAT are thsoe who take it somewhat seriously and have jumped through (minor) hoops to take it. As opposed to public schools where it may be a given that high schools take it.