He can apply just as many many students do for acceptance at the most selective schools in the country. If he wants to be at a college next year, he should also apply to other less selective schools, also as should any student who wants to go away for college next year.
In that respect, he is no different from other college applicant. His age is not going to be an advantage at all in the process, nor is his home school status. Whether a college uses any filters in assessing way younger than usual kids as residential admits comes down to individual schools.
Few kids that age are considered optimal candidates for the general dormitories, and most parents would not want a young teen kid of that age thrown into that mix. Your child, is not used to spending the bulk of the day mixing with the general population of a school with kids his age and if that age gap, as it is. You suddenly want to throw him into close 24/7 quarters into the late teen and young adult population, particularly known to indulge in risky experimentAction and flights into madness?
Some schools have had experience in dealing with this situation as parts of official studies; JHU and CMU come to mind. But still, most of those kids, especially at the younger end of the spectrum commuted.
By very definition, the odds of your son, or any student getting into the top 10-15-20 colleges are very small. Though his academic profile is right up there, the rest of the info shared is weak for a top school candidate. No hook there either. So if college work is the goal, make sure some more likely schools are in the list.
Since your son appears to enjoy accelerating his academic studies, a full service university with doctoral programs in his fields of study and interest are what I’d suggest. That way , the ceilings are very high and even nonexistent in available academic opportunities. Pick such schools, and certainly include top schools with low accept rates if they fall on the list, but understand that finding schools with likely accept rates to add to the list is even more important for him to realistically have choices when the decisions are released.
I once worked in a program for academically advanced students, who were up to college level courses in difficulty level. There are quite a few kids in this am category; your son is not unique in this regard, nationally, though he may be locally. Most of these kids were not accepted into highly selective school but did find college courses and programs that allowed them to advance educationally. The conclusion of the program was that statistically, these kids did well, as did most of those at that academic level that continued in higher education but no outstanding results in the pools that got special entry to programs geared to them at the few highly selective schools that did give special attention to these circumstances.