For research, take a look at the National Writing Board and the Concord Review:
See also:
http://talk.collegeconfidential.com/college-admissions/527787-national-writing-board.html
For internships, the NY Historical Society also has year-round and summer-only internships:
http://www.nyhistory.org/education/internships/high-school-internships
See also:
http://www.nahyp.org/awardees/student-historians-high-school-internship-program/
And the National Museum of American History at the Smithsonian has internships during the school year and summer as well (the summer deadline is February 1):
Finally, the College of William and Mary has a pre-collegiate summer program in Early American History:
http://www.wm.edu/as/niahd/precollegiatesummer/index.php
Those should give you some starting options.