Character with Autism. Realistically portrayed?

Okay, here's the thing: In an attempt to broaden my character array, I thought of including a character with a mental issue of some kind, and, after some research, I chose autism, because everyone else in the group has their own antisocial tendencies to work out.

Rundown: This is a world where people have powers. The Hero has the power of Mega Manning, and so goes about learning from people wherever he can. This girl has Shock and Awe (would that technically be Psycho Electro?), and he thinks it would be a useful power.

Basically, every day, she goes to a certain spot at a certain time and starts shooting lightning at things. And the Hero shows up when she shows up, not engaging her in conversation or anything, and just copying what she does. This goes on for a few days to maybe a bit over a week, until she tells him that he's not doing the form right, then explains how it should work. That goes on for a few days, until one day she misunderstands him and gets nervous and runs away. Next day, she apologizes for making him "angry," and eventually, he starts wearing one of those white-face masks that's permanently smiling.

I want to know if any of the above paragraph is not in-keeping with the way an autistic person would respond, either she's too calm or too erratic.

There's also the issue of getting her to join in the group in the first place, since the constant change of venue could be distressing for her.

(Disclaimer: My brother has an Asperger's Syndrome-like autism, and I have some of the traits myself, but I don't claim to be an expert on the subject. I might be mistaken in some of these things.)

Well, every person is different, but off the top of my head I'd say she wouldn't immedially apologize to him. Running away would be her way of ending an uncomfortable interaction, and once she has done this she wouldn't consider it an issue anymore.

Autists often have trouble picking up on facial expressions, tone of voice, sarcasm and other indicators of mood. People will have to tell her excactly what they're feeling, otherwise she'll get confused. She'll probably have issues with eye-contact as well, but as for psysical contact, it could go either way. Some find safety and comfort in touching and hugging, others feel the exact opposite. These are just some ideas to how you could write her interacting with others.

As for the stress with changing venues, this is tricky. You could give her a "safety spot" or item she can use when life gets too stressful. Like a blanket to put over her head.