Welcome!

The forum has many parents with a similar experience to yours. You are asking great questions, and will probably get a wide variety of answers as what works may be different for each family/child/school combination.

In general, play-based preschool is preferred to a preschool experience based on academics. Does the program which you selected for your child offer ample opportunities for play when your child demonstrates that he knows what is about to be taught?

For locating a child psychologist, many find the lists at Hoagies a good place to start: psychologists and professionals familiar with the gifted.