DeeDee, you asked some great questions. DS had another assessment done at 4.5 and 5.5 by two different educational psychologists, both of whom said they do not think DS is on the spectrum. I still see some characteristics, but then between possible ASD, ADHD, giftedness, SPD, and who knows what else, it is hard to figure out exactly what is going on! Currently he has no diagnosis other than being highly gifted.
Our experience is that it's sometimes hard for professionals to see autism in a child who is gifted, not least because if the child's verbal skills are strong the autism presents in a non-standard way.
Regardless of dx/non-dx, ABA or other behavioral strategies are going to be your best bet for getting a handle on behavior. Working on this in early elementary clears obstacles and lets the gifts shine better in late elementary/middle.
Hang in there.
