my son does not have friends in school. It seems that he has below-average ability to make friends.
I wouldn't be so quick to jump to this conclusion when looking at the information you have presented. He may be above-average in ability, but be placed in a situation that even overcomes those 'above-average' skills.
Having an IQ that is 3 to 4 SD beyond the other kids isn't exactly like being 3 or 4 years older, but it is close enough for a thought experiment to get an example of what I mean from above.
Let's say that one of the more ND (normally developing) kids in his classroom, age 6, returns to school in September 2011 to find that she has been placed in a preK room with 3 year olds. No explanation. The teachers don't seem to recognize that her readiness to learn zone is 3 years advance of the other children so all the daily activities are appropriate to ND 3 year olds. How would an average 6 year old with average 'friend making' abilities do? Zoom forward in time 7 months and the situation is the same - how is our thought experiment child doing now?
If you compare how your son has done to the child in the thought experiment, you might decide he has above average 'friend-making' skills.
We have a few posters from Chicago. You might find that on a playdate with one of those children, your son looks like a completely different kid. Chicago also has 'Saturday enrichment classes' that might have kids who have 'playdate potential.'
Handwriting at age-average is totally normal for gifties - although there are a few who are well above average. This is where the above 'age+3' analogy breaks down. Some have above average athletic ability, and some have 'just' age-average.
Good luck with the school search. Remember that some local public district in the Chicago area have many gifted kids in them, and that a private school that markets itself to 'the gifted' may not have more advanced kids than your local public school. What you want is a school that can recognize advanced abstract reasoning skill in young children and a school that is Flexible. A school that can look at the test scores and say - Let's roll up our sleeves and get to work modifying our offerings. It's not unusual for PG kids to need a full grade skip and a subject acceleration or two while at a private school for gifted - because PGs are so rare that who could make a living restricting a private school to just PG kids?
If I ran a Gifted school, the first thing I would do is sit down with the child and the end of year tests and see what level the child is at in each subject. I wouldn't assume that age is a good proxy for readiness to learn level.
Love and More Love,
Grinity