How do you separate neurological from mental, when mentality is based on a neurological substrate?
What you are most likely seeing are the abilities of a fraction of ASD's to be able to mimic social signalling of various forms.
Not necessarily. One may have two or three very extreme recognised conditions, another may have six or eight milder one's, and both may not have the same individual conditions, and yet both be in the same ASD group. I don't think the current system of diagnosis has much to do with the individual conditions that can put a person in the autistic spectrum, but rather to do with the outcome of having one or more of a class of neurological condition.
I don't think of autism as a condition really, but rather a class of symptom caused by a class of varying and variable neurological/developmental conditions.
You're making too much out of the different groups, 1, 2 and 3, imho. I think these are far more focussed on diagnosing who needs appropriate therapy and what sort of therapy (and support), not on specific symptoms in themselves.
The type, number and severity of symptoms can provide an almost infinite range of possibilities (try throwing 6 20-sided dice and see how many combinations of results you can get) - these don't just slot into one of three categories, we're people like you, and infinitely variable like you, the categories are medical devices to provide the best levels of care to the most needy in an environment of insufficient resources - in other words they are a way of making something incredibly complex into a simpler form to allow an attempt at fair distribution of services to those most in need (just like with almost every other malady, but more complex and less well understood and early efforts rarely hit the nail on the head in medicine).