To meet criteria for Autism Spectrum Disorders (ASD), people have to meet X number of symptoms (which can range in severity each) out of Y total number of symptoms. SO, there ends up being a lot of combinations of how things end up for each individual. Not everyone will have the eye contact issue and for some it is subtle.
As far as touch....kids on the spectrum often have sensory integration issues and social boundary issues. My son is like your difficult child. He is way too into people's space. Touches too much and does not know the degree of touch he applies so he is cued daily on gentle or staying an arms length away etc. He would hug everybody and has in past knocked people down with enthusiastic hugs. He has always squished flesh like arms and tummies when he hugs or touches people. Just likes that squish feel (so we use "figits" to replace that need with something appropriate to squish). My son has had eye contact issues on and off and now looks more like he is shy at times. He has really great eye contact most of the time now. Especially when comfortable. Even some doctors and psychologists still use that as a standard sign but anyone who has been around many people with Autism Spectrum Disorders (ASD) knows that is a highly variable symptom.
OH, and as far as touch....even kids who love to touch, sometimes really only like it ON THEIR TERMS....they initiate it and may pull away if someone else, especially a non parent, wants to touch or hug them. Again, that is variable, but it is something you will see/hear of a lot.
Touching a lot of things, can sometimes be viewed as adhd behavior and it can also be "sensory seeking" in that they do not register touch as much and need more and more input to feel "right". Occupational therapy can really help with this!