My son from the time that he was a baby would pick at our thumbs at sleep time. I did not think anything about it until he would get upset if you did not let him do it. Later he developed the rocking and hand flapping. Although he does speak, it is very jumbled, he is now 7 almost 8 but is developmentally that of a 4.5 year old. He has no social abilities, for he does not grasp subtle clues. I have yet to get a full diagnosis for him, I went through social security to get some clue as to what is wrong, yet I disagree to an extent of what they say. The doctors say that he is fine and will catch up, but 4 years later and therapy has not help. He is now in danger of failing the first grade because he can not possibly keep up.I suspect that he has an auditory deficit. He hears perfectly well, yet his brain does not seem to interpet the right messages. My advice is to get help asap, and do not settle for he'll catch up. If you suspect that something is wrong keep on fighting. Its a long fight but you the mother know your child better than a doctor
Have a look at the DSM IV diagnostic criteria for a diagnosis of autism.
Also speak with the Speech Therapist. Make sure she has experience of speech disorders as well as developmental disorder such as Autism. She should be able to tell you if the speech and language difficulties he has are consistant with a diagnosis of being on the autistic spectrum. She is also the professional to assess for social interaction and skills.
When you say confrontations in play, do you mean he wants it to go how he wants and cannot accommodate other childrens input into how the game or play should go? That can be seen in children on the spectrum. They tend to be less flexible and have a rigid idea of how the game should go. Sometimes they even want an exact repetition of something they have already seen.
Hand flapping and spinning is a behaviour that is on the spectrum. But some children do that who aren't on the spectrum. There are also children on the spectrum who don't show those behaviours.
I would look at the diagnostic criteria, make a note of all the things you are concerned about and speak with the Speech Therapist and your child's paediatrician.
If you want an assessment ask to be referred to a multi disciplinary team that has experience of diagnosing autistic spectrum disorders.