Yale BA/PhD here. There's a lot of hypothesizing and wishful thinking floating around this thread. Yale requires 36 credits to graduate. In almost all circumstances, 1 credit = 1 semester-long course. (A few courses, such as intensive language courses that guide students through two years of language courses in a single year, carry 2 credits; in my experience these courses take much more than twice as much time and effort as a 1-credit course!) Under normal circumstances, students take nine courses per year: four one semester and five the other. Yale doesn't accept part-time students; not only do you have to take at least three courses in any one semester, you will only be promoted to your next year's standing if you are keeping up an average of 8-9 courses per year.
Those 36 credits must ordinarily be completed in no more than 8 semesters of enrollment, and no fewer than 6. You can't take a lighter courseload or enroll part-time in order to extend your degree over more than 8 semesters of enrollment, although you can take a leave of absence. You can only transfer a maximum of 2 credits from another university (unless you're doing a full-time study-abroad semester or year through the university)--and only if you're planning to graduate in 8 semesters; you can't use credit earned elsewhere to speed up your graduation. You can apply a maximum of 4 online summer courses
taught by Yale to your degree. All other online courses fall under the rule about transferring a maximum of 2 external courses.
In practice, course offerings in the summer are far more restricted than those in the academic year proper (fall and spring semester). A student would be unwise to expect to be able to complete her major requirements by relying heavily on summer courses.
You can use AP credits to accelerate your graduation if you're planning to graduate in fewer than 8 semesters, but not to reduce the number of courses you take per semester. Your AP credits can be used to place into certain advanced courses instead of beginning with an introductory course, but they can't count toward your major requirements or any of the distributional requirements (the general education requirements that apply to all Yale undergraduates, regardless of major).
All these rules, and many more, are laid out here:
http://catalog.yale.edu/ycps/academic-regulations/
I can also say from experience that Yale does not make it easy to bend these rules. They have no reason to. They're not interested in making it easier to earn a Yale degree. They're interested in guaranteeing that the degree and the university maintain their reputation as among the best in the world, by upholding the extremely high quality of both the education they offer and the graduates they produce.
On a lighter note, one reason that Nathan might decide to go to Yale now is that all students live on campus for their first two years, and most live on campus for all four. Freshmen are assigned to one of twelve "residential colleges", where for the next four years they live, eat in the dining halls, work out in the basement gyms, attend informal visits by interesting people hosted by faculty who live in the colleges ("Master's Teas"), play on intramural sports teams...the list goes on and on. It would be much easier and probably more enjoyable to immerse himself in that environment now than it would be once he were four or five years older than his fellow freshmen (let alone fourteen or fifteen).
And while we are technically Elis, I've never seen or heard that term used outside the New York Times crossword puzzle. We generally go by Yalies these days. Our sports teams are the Bulldogs, and our mascot, Handsome Dan, is a real live bulldog and, in my totally unbiased opinion, the most adorable puppy ever:
http://www.yalebulldogs.com/information/mascot/handsome_dan/index
Congrats to Nathan! I hope he has a wonderful time at Yale and finds the time to sample all the university and the town have to offer--including New Haven's legendary pizza.