Most programs that run HS competitions do have
their own stashes of HS questions that for the most
part you'd have to purchase from them. CWRU for
example has electronic copies of all their HS tournaments
questions from 1996-1999 High School Celebrity Shoot and
1997-1999 Great Lakes Regional Academic Championship that
you can get for $10. I'm sure other programs such as
Maryland-College Park, Princeton, Yale, Bowling Green, and
Cal-Berkeley (among others) may have other questions you can
get from them.