Speaking here as the parent of a 2E/autistic:
Lovely that your DS is excited about academic learning. Along with the reading/math skills he is so motivated to pick up, I'd want to make sure that he's learning to enjoy things the way other kids do. If his interests are restricted (which it sounds like they may be from your pool incident) he won't pick up play skills that are important for building thinking and social skills. He should be not only reading at the pool, but also learning to like the water. Not only counting toys, but learning to play with them and pretend. This isn't "kid stuff"-- it's a foundation for many other things.
The obsessive quizzing language is a concern for me. As a parent I'd make sure to be engaging him in two-way conversation that does not take the form of quizzing or tutoring. You don't want his main means of engaging other kids to be quizzing.
I think it would be fine to keep him home from day care/preschool another year if that's what you want to do, but I would definitely work on increasing exposure to other kids, as well as many different environments. Learning to be "OK with it" is a major life skill.
