Hand flapping and other types of stereotypy are common in children who have developmental disabilities regardless of whether they have autism. If you are concerned about your daughter's diagnosis I would suggest that you identify a hospital in an urban area where they specialize in diagnosis of children who present developmental delays. A comprehensive evaluation by a team of specialists will result in diagnostic information as well as treatment recommendations. You can then take these recommendations to your local early intervention program.
My son hardly ever hand flaps, infact I only see it about once a week. But he did use to spin as a toddler. Apart from hand flapping your daughter could be showing signs of echolalia. This is when questions/phrases said to the child are repeated back by the child. Delayed echolalia is when a child repeats DVD/TV dialogue either to themselves or uses it as a form of communication.
My son also gave answers to questions 'off topic'. This was (a) communication disorder - he simply did not know what I was asking him but knew I was expecting an answer from him. So if we were reading a book and I asked him 'what is the man doing' (answer: washing the car), my son would say 'it is red' (the colour of the car in the book was red). Or he used an echolalic response to my question.
My son also has empathy, sense of humour, theory of mind, appropriate facial expressions (although maybe not to a level of a 'normal' child).
It is quite possible to have autistic traits, but not enough of them in all the areas required for a clinical diagnosis. But I think you do need to mention your concerns to professionals.
My daughter has many of the same manners as both Sally44 and Gayahnda have described. Her main area of issue is in her speech- she just turned 7 and has been in years (since 3) of speech therapy through Texas Children's Hospital and is still having difficulty staying on topic, relating to peers, expressing ideas and feelings. Now she stutters painfully through any thought she's trying to convey. Her kindergarten teacher and school faculty believed she had autism; this was ruled out after extensive testing through Tx Children's Learning Support Center. I've not received a definite diagnosis and have only been told she has a speech delay. I'm very concerned about her future. I feel desperate at times to know how to help her because she struggles with academia and social interaction. I took her out of public school and put her into Private Montessori School hoping the smaller class rooms would help make a change but it hasn't. I would like to know what to do next.
It might help to look at the 'clinical' diagnostic criteria for autism. Find out which you use if you are in the states. Or you can look at DSM IV 299 for criteria for autistic spectrum disorders. I think it would then be useful for you to go through that with an appropriate professional to identify which parts of that criteria your daughter might fit. Take with you a list of behaviours you have noticed with your daugther that you think are autistic and also list your concerns. It is quite possible to have several autistic traits, but not enough of them in each criteria to reach a diagnosis. But where your daughter does match the criteria eg. speech/social communication, then they could use the same strategies they might use for an autistic child.
When my child was first assessed by Speech/Language professional she told me straight away that with that kind of speech problem it is usually autistic spectrum disorder eg. not understanding pronouns (I, me, you, she, he, his, hers, they, them etc); difference in receptive/expressive language (expressive language at age 7, receptive at age 3) and echolalia. However it took 18 months in total to get a diagnosis because the only way to find out if they are on the spectrum is to watch them over a long period of time.
Does your child have any problems with transitions (moving from one activity to another at home or in school/having to stop watching TV. Does she play with toys in the 'normal' way and not play with bits of toys. Does she talk to herself and giggle or re-enact/repeat things she has seen on TV.
When you say she speaks off topic to you mean she gives the wrong answer to the question or does she talk alot about certain topics that she is interested in regardless of whether it is relevant or whether anyone else is interested.
Does your child have any 'over emotional' responses to things you think are quite trivial. She she get upset/angry for no apparent reason. When she plays with other children is it 'alongside' them but not fully interacting with the other children in the game. Does she have problems understanding the rules of the game or having to change her role within the game.
If, having spoken again with professionals (I believe your Paediatrician and through school) and your daughter does not fit all the criteria for any condition then I think you could ask under which diagnosis would her traits 'fit' and ask for supports relevent to those traits to be used in school.