Your child's diagnosis is still relatively new and it sounds like you are still adjusting to everything it means. That's OK, it's a process, it takes time.
If you are uncomfortable with what the therapy student is saying or doing, have an honest talk with her. Explain your feeling about these issues. Has her if they have covered topic this in her classes at all. If she wants to pursue this field, so is going to learn how to talk with the parents of her clients.
As Catherine said, a lot of people in the autism community prefer the term autistic. There are people who feel strongly on both sides of the issues. A lot of it has to do with how you choose to think about autism.
Personally, I don't buy into the "person-first" language thing. I think it sounds awkward, contrived, and actually puts a more negative emphasis on autism. My son is an autistic child. He is also a blond child, a smart child, a sweet child, and a Catholic child. None of those things define who he is, but they all play a role in his identity and in who he is as a complex, individual person.
I did, and still do, find it helpful to hear about other autistic children, and how they were (are) similar to DS. It helped me to know that we were on the right track with the things we were doing. And it gave me comfort to know that there are other people like him in the world, which means there is a community he can belong to and fit in. A few days ago, DH and I delighted in reading a blog article about a child who is very similar to our son. It's good to know that there are more like DS out there.
None of this means that you are wrong to feel the way you feel. You might find over time, that your feelings about these issues (and others) may change. But how you feel right now is valid and needs to be addressed. Take the time to talk to the student and help her see your perspective.
Good luck. Hugs.