A lot of the symptoms seem language based, like the echolalia (repeating what you say) and babbling. This could be part of verbal dyspraxia or some other speech impairment. Seeming not to hear you could also be a speech/processing thing, or attention. I don't know what his receptive language is like, but if he doesn't seem to understand you or look at you it could be that he doesn't really understand what you are saying. If there seems to be receptive problems, look up developmental dysphasia. When I read about this, a lot of the symptoms are very autistic like. This could only be language, so I wouldn't jump to autism yet. What does concern me is the door thing and the walking on toes. These could just be things that he likes to do for whatever reason, however it isn't typical behavior.
He would be worth watching, but it just may be language based. If you are AS he could have some neurological similarities but not to the extent for it to be AS. I have AS traits, however I'm definately NT.
Good luck! At least he has you to understand him if he does end up on the spectrum!